### Part 1:

The temperature of a pie is $430$ degrees Fahrenheit when it is first removed from the oven. After $4$ hours the temperature of the pie is $97$ degrees fahrenheit.
Derive an exponential formula $f(t)$ for the temperature of the pie as a function of time, $t$ in hours. Round all your calculations to $4$ decimal places.
Here’s how:
Since we are asked to find an exponential formula, we know the formula is going to look something like
$f(t) = ab^{t}$
We know the temperature of the pie at two different times including the initial temperature.
Goal: find values for $a$ and $b\text{.}$
1. $a$” is given in the problem.
What is the initial temperature of the pie? $a =$ degrees Fahrenheit.
2. Next, we will find the overall growth factor and use it to determine the hourly growth factor $b\text{.}$
The pie decreases in temperature from $430$ degrees to $97$ degrees. What is the overall growth factor associated with this temperature decrease?
The overall growth factor is:

Solution: