A potato is placed in a preheated oven to bake. Its temperature *P* = *P*(*t*) is given by the following.

*P* = 400 − 325*e*-*t*/50

The given equation represents the temperature \( P(t) \) of the potato as a function of time \( t \) in minutes:

\[
P(t) = 400 - 325e^{-t/50}
\]

Here’s a breakdown of the elements in the equation:
- **\( P(t) \)**: The temperature of the potato at time \( t \).
- **\( 400 \)**: The ambient or steady temperature of the oven.
- **\( 325e^{-t/50} \)**: The exponential decay term, where the temperature rise slows down as time passes, and \( e^{-t/50} \) represents the rate of cooling or heating.
- **\(

A potato is placed in a preheated oven to bake. Its temperature P = P(t) is given by the following: P = 400 − 325e^-t/50

Understand how to model the temperature of a baking potato using an exponential decay function. This problem covers the concept of temperature as a function of time with the formula P(t) = 400 − 325e^-t/50, illustrating key exponential decay principles. Suitable for students in Grades 11-12.

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