Concept Byte: Using Logarithms for Exponential Models

For Use With Lesson 7-5

TECHNOLOGY

You can transform an exponential function into a linear function by taking the logarithm of each side. Since linear models are easy to recognize, you can then determine whether an exponential function is a good model for a set of values.

If log b and log a are constants, then log y = ( log b ) x + log a log y equals open log b close x plus log eh  is a linear equation in slope-intercept form when you plot the points as (x, log y).

Activity

Determine whether an exponential function is a good model for the values in the table.

Step 1 Enter the values into stat begin box , stat , end box  lists L 1 cap l sub 1  and L 2 . cap l sub 2 , .  To enter the values of log y, place the cursor in the heading of L 3 cap l sub 3  and press log begin box , log , end box   L 2 cap l sub 2   enter . begin box , enter , end box , .

Image Long Description

Step 2 To graph log y, access the stat plot begin box , statplot , end box feature and press 1. Then enter L 3 cap l sub 3  next to YLIST:. Then press zoom begin box , zoom , end box  9.

Step 3 Press stat begin box , stat , end box   ► 0 u 2 0   enter begin box , enter , end box to find the exponential function y = 0.5 ( 2 ) x . y equals 0.5 . open 2 close to the x . .

Exercises

For each set of values, determine whether an exponential function is a good model. If so, find the exponential function.

1. x	1	3	5	7	9
   y	6	22	54	102	145

2. x	− 1 negative 1	0	1	2	3
   y	40.2	19.8	9.9	5.1	2.5

3. Writing Explain how you could determine whether a logarithmic function is a good model for a set of data.

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