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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