A can of soda is placed inside a cooler As the soda cools it

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) = -22 + 42e-^-0.034x Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary. Initial temperature: degree C Temperature after 20 minutes: degree C

Solution

T(x) = -22 + 42 e^ - .034 x

initial temperature is the temperature when x = 0

so plugging x =0 in the equation

T(x) = -22 + 42 e^(-.034*0)

initial temperature = 20 degree celcius

temperature after 20 minutes

plug x = 20

T(x) = -22 + 42 e^ - .034(20)

T(x) = -22 + 21.2779

temperature after 20 minutes = - 0.7221 degree celcius