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File: Solving Equations Pdf 178486 | Nc Math1 06 06
name date 6 6 solving exponential equations for use with exploration 6 6 essential question how can you solve an exponential equation graphically 1 exploration solving an exponential equation graphically ...

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                      Name _________________________________________________________    Date __________  
                          6.6  Solving Exponential Equations 
                                       For use with Exploration 6.6 
                      Essential Question  How can you solve an exponential equation 
                      graphically? 
                        1    EXPLORATION: Solving an Exponential Equation Graphically 
                           Go to BigIdeasMath.com for an interactive tool to investigate this exploration. 
                           Work with a partner. Use a graphing calculator to solve the exponential equation 
                            2.5x−3 = 6.25 graphically. Describe your process and explain how you determined  
                           the solution. 
                            
                            
                            
                        2    EXPLORATION: The Number of Solutions of an Exponential Equation 
                           Go to BigIdeasMath.com for an interactive tool to investigate this exploration. 
                           Work with a partner. 
                                                                                          x
                                                                                   y = 2.
                              a.  Use a graphing calculator to graph the equation            
                                                                             6
                       
                                                              −6                           6
                                                                            −2
                              b.  In the same viewing window, graph a linear equation (if possible) that does not 
                                                               x
                                                         y = 2.
                                  intersect the graph of          
                       
                              c.  In the same viewing window, graph a linear equation (if possible) that intersects 
                                  the graph of  y = 2x  in more than one point. 
                       
                              d.  Is it possible for an exponential equation to have no solution? more than one 
                                  solution? Explain your reasoning. 
                       
                      Copyright © Big Ideas Learning, LLC                                        Integrated Mathematics I      173
                      All rights reserved.                                                            CopyrStudent Jouight © Big Idears Lnalea rning, LLC
                                                                                                                     All rights reserved.
                                                                     213
        Name _________________________________________________________   Date _________  
           6.6   Solving Exponential Equations (continued)
             
          3   EXPLORATION: Solving Exponential Equations Graphically 
            Go to BigIdeasMath.com for an interactive tool to investigate this exploration. 
            Work with a partner. Use a graphing calculator to solve each equation. 
                  2x = 1                     x+1                        x
               a.                        b.  20=                   c.         
                       2                                              21=
         
         
         
                   x                         x−1                      42x = 1
               d. 39=                    e.  30=                    f.      16  
         
         
         
                   3x   1                    x+2   1                    x−2  3
                  2  =                      3    =                    22=−x
               g.       8                h.        9                i.       2       
         
         
         
              Communicate Your Answer 
               4.  How can you solve an exponential equation graphically? 
         
         
               5.  A population of 30 mice is expected to double each year. The number p of mice in 
                  the population each year is given by  p = 30 2n . In how many years will there be 
                                                     ()
                  960 mice in the population? 
         
         
              Integrated Mathematics I                                 Copyright © Big Ideas Learning, LLC 
        174
       Copyright © Big Ideas Learning, LLC                                         All rights reserved. 
              Student Journal 
       All rights reserved.
                                                      214
                          Name _________________________________________________________    Date __________  
                               6.6  Practice 
                                              For use after Lesson 6.6 
                          Core Concepts 
                          Property of Equality for Exponential Equations 
                                                                                                           b ≠ 1,
                          Words               Two powers with the same positive base b, where                       are equal if 
                                              and only if their exponents are equal. 
                                                   x      5                      x = 5,           x       5
                          Numbers If   then x = 5. If                                     then 2 = 2. 
                                                 2 = 2,
                                                               b ≠ 1,            x      y
                          Algebra If  and                                then bb=          if and only if  x = y. 
                                                 b > 0
                           
                          Notes: 
                     
                           
                           
                          Worked-Out Examples
                          Example #1
                          Solve the equation. Check your solution.
                              9x     7x+8                              9x     7x+8
                           3  = 3                  Check: 3  = 3
                                                                      9(4) ?  7(4)+8
                           9x = 7x + 8                              3     = 3
                                                                          ?
                                                                       36     28+8
                           − 7x − 7x                                  3  = 3
                                                                       36     36
                           2x = 8                                     3  = 3
                             2x     8                                  17                    17
                                    —
                                                       1.50095 × 10  = 1.50095 × 10  ✓
                                  =     
                             — 2
                              2
                        x = 4
                           
                          Th  e solution is x = 4.
                                                                                                                   Integrated Mathematics I 
                                                                                                                          Copyright © Big Ideas Learning, LLC
                                                                                                                                                       175
                                                                                                                                            All rights reserved.
                                                                                                                                Student Journal 
                                                                                  215
                     
                         
                                                                  Name _________________________________________________________   Date _________  
                                                                                      6.6                                                          PracticePRACTI(CcoEnytinued)
                                                                 Example #2
                                                                Solve the equation. Check your solution.
                                                                                                                                                                                                               1 x+1
                                                                                                                                   −3x+3                                                             —
                                                                   36  =                                                                                                                                                                                    
                                                                                                                                                                                                                               )
                                                                                                                                                                                               (216                                                                                                                                  Check:                                                                                                                                                                                    
                                                                                                                                                                                                         1 x+1                                                                                                                                                                                                                                                                                                    x+1
                                                                                                                        2 −3x+3                                                                      —                                                                                                                                                                                                                                                                                      1
                                                            (6)                                                                                                          =                                                                                                                                               
                                                                                                                                                                                                                    )                                                                                                                                                                                           −3x+3
                                                                                                                                                                                               ( 3                                                                                                                                                                                                                                                                                —
                                                                                                                                                                                                                                                                                                                                      36                                                                                                              =                                                                          
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            )
                                                                                                                                                                                                     6                                                                                                                                                                                                                                                                     (216
                                                                                                                     2(−3x+3)                                                                                −3 x+1
                                                            6                                                                                                            = (6                                               )                            −3(3)+3? 1   3+1
                                                                                                                                                                                                                                                                                                                                      36                                                                                                              =                                                                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
                                                                                                                     2(−3x+3)                                                                          −3(x+1)                                                                                                                                                                                                                                                                   —
                                                            6                                                                                                            = 6                                                                           (216)
                                                            2(−3x + 3) = −3(x + 1)                                                                                                                                                                                                                                                                                                                                    −9+3 ?                                                               1                     4
                                                                                                                                                                                                                                                                                                                                      36  =             
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 —
                                                            2(−3x) + 2(3) = −3(x) − 3(1)                                                                                                                                                                                                                                                                                                                                                                                   (216)
                                                                                                                                                                                                                                                                                                                                                                                                                                     −6 ?                                              1                                       
                                                                                                                                                                                                                                                                                                                                      36  =        
                                                                                                           −6x + 6 = −3x − 3                                                                                                                                                                                                                                                                                                                                              —
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          2164
                                                                                                      + 6x   + 6x                                                                                                                                                                                                                                                                                                                                            ?
                                                                                                                                                                                                                                                                                                                                                                                                                                       1                                                                                1                                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                     =                                                                                                                       
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                              — ——
                                                            6 = 3x − 3                                                                                                                                                                                                                                                                                                                                                         366                                       2,176,782,336
                                                                                                                                             + 3   + 3                                                                                                                                                                                                                                                1                                                                                                                  1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         ——
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ✓
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                        =   
                                                            9 = 3x                                                                                                                                                                                                                                                                                     ——2,176,782,336
                                                                                                                                                                                                                                                                                                                                                       2,176,782,336
                                                                                                                                                                9                              3x
                                                                                                                                                                                              —
                                                                                                                                                                                                             
                                                                                                                                                                                                                 
                                                                                                                                                                           =   
                                                                                                                                                               —                                   3
                                                                                                                                                                3
                                                            3 = x
                                                                  Th  e solution is x = 3.
                                                          Practice A
                                                                Extra Practice 
                                                                
                                                                In Exercises 1–15, solve the equation. Check your solution. 
                                                                
                                                                                                                       4x                                            12                                                                                                                                                                                 x+5                                                    20                                                                                                                                                                         45x−                                                          2x
                                                                                    1.  33=                                                                                                                                                                                                                          2.  88=                                                                                                                                                                                                                          3.  66=                                                                                                           
                                                                
                                                                
                                                                
                                                                 
                                                                                                                     6x−3                                                         −+34x                                                                                                                                                                 2x+11                                                                                                                                                                                                                           3−2x
                                                                                  4.  55=                                                                                                                                                                                                                          5.  4                                                                       = 1024                                                                                                                                                6.  8                                                                 = 512 
                                                                 
                                                                
                                                                 
                                                                 
                                                                 
                                                                                                                       7−x                                                                                                                                                                                                                                        x−2                                                                                                                                                                                                                             6x−1                                                        5x
                                                                                    7.  4                                                            = 256                                                                                                                                                           8.  49                                                                     = 343                                                                                                                                                 9.  36                                                                        = 6  
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                                                                        x−43x                                                                                                                                                                                                                                     x+1                                                                     x                                                                                                                                               2x                                                       21x+
                                                                  10.  9                                                                             = 81                                                                                                                                                   11.  64                                                                          = 512                                                                                                                                            12.  6                                                            = 36                                                            
                                                                 
                                                                                                                Integrated Mathematics I                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Copyright © Big Ideas Learning, LLC 
                                                                  176
                                                        Copyright © Big Ideas Learning, LLC                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     All rights reserved. 
                                                                                                                Student Journal 
                                                        All rights reserved.
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...Name date solving exponential equations for use with exploration essential question how can you solve an equation graphically go to bigideasmath com interactive tool investigate this work a partner graphing calculator the x describe your process and explain determined solution number of solutions y graph b in same viewing window linear if possible that does not intersect c intersects more than one point d is it have no reasoning copyright big ideas learning llc integrated mathematics i all rights reserved copyrstudent jouight idears lnalea rning continued each e f g h communicate answer population mice expected double year p given by n many years will there be student journal practice after lesson core concepts property equality words two powers positive base where are equal only their exponents numbers then algebra bb notes worked out examples example check th practicepracti ccoenytinued...

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