Part 1:

The temperature of a pie is [math] degrees Fahrenheit when it is first removed from the oven. After [math] hours the temperature of the pie is [math] degrees fahrenheit.
Derive an exponential formula [math] for the temperature of the pie as a function of time, [math] in hours. Round all your calculations to [math] decimal places.
Here’s how:
Since we are asked to find an exponential formula, we know the formula is going to look something like
[math]
We know the temperature of the pie at two different times including the initial temperature.
Goal: find values for [math] and [math]
  1. [math]” is given in the problem.
    What is the initial temperature of the pie? [math] degrees Fahrenheit.
  2. Next, we will find the overall growth factor and use it to determine the hourly growth factor [math]
    The pie decreases in temperature from [math] degrees to [math] degrees. What is the overall growth factor associated with this temperature decrease?
    The overall growth factor is:

Solution:

Part 2: