Question

A can of soda is placed inside a cooler. As the soda cools, its temperature T(x) in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x) = -20+38e^-0.41xFind the initial temperature of the soda and its temperature after 15 minutes. Round your answers to the nearest degree as necessary.

Answer 1

Solution:

Given the function:

$T(x)=-20+38e^{-0.41x}$

At initial temperature, x=0. Then;

$\begin{gathered} T(0)=-20+38e^{-0.41(0)} \\ \\ T(0)=18 \end{gathered}$

The initial temperature is 18 degrees Celsius.

Also; after 15minutes, x=15. Then;

$\begin{gathered} T(15)=-20+38e^{-0.41(15)} \\ \\ T(15)=20 \end{gathered}$

ANSWER: After 15 minutes, the temperature is at 20 degrees Celsius.