T(x)=−20+42e-0.45x

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+42e^-0.45x

 

Find the initial temperature of the soda and its temperature after 18

minutes. 

Round your answers to the nearest degree as necessary.

Answer 1

When the soda is initially placed in the cooler x = 0. Thus T(0) = -20 + 42 e ^ (- 0.45x). The exponent becomes 0 and all numbers to the zero power equal 1. Thus T(0) = -20 + 42 = 22.

When x = 18 the equation becomes T (18) = -20 + 42 e ^ (-0.45 * 18) .

Multiplying to have the exponent value -0.45 x 18 = - 8.1.

e to the - 8.1 is 0.0003035.

This number multiplied by 42 is 0.01275.

Subtracting 20 give the answer as -19.987.