Algebra 2 Companion Book, Volume 2

7.2.4 Curve Fitting With Exponential and Logarithmic Models − Worksheet

Example 1: Determine whether f is an exponential function of x of the form f ( x ) = ab x . If so, find the constant ratio. 1. 2.

x

x

− 1 0 1 2 3

− 1 0 1 2 3

5 7

1 3

f ( x ) − 2

f ( x ) 27 18 12 8

− 1 11 95 683

5

3.

4.

x

x

− 1 0 1 2 3

− 1 0 1 2 3

f ( x )

1 4

1 3

1 9

5 1

− 3

− 7

− 11

f ( x ) 2

3 4

5

7

Example 2: 5.  The table gives the approximate number of degrees Fahrenheit above room temperature of a cup of tea as it cools. Find an exponential model for the data. Use the model to estimate how long it will take the tea to reach a temperature that is less than 40 degrees above room temperature. Cooling Tea Time (min) 0 1 2 3 4 Degrees above room temperature (ºF) 132 120 110 101 93 Example 3: 6.  The table shows the population milestones for a small town following its incorporation. Find a natural log model for the data. Use the model to predict how long it will take for the population to reach 8000. Town Population Milestones Time (mo) 6 18 42 90 150 Population 3000 4000 5000 6000 7000

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