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 o

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)=-22+46e^(-0.03x) Find the initial temperature of the soda and its temperature after 15 minutes. Round your answers to the nearest degree as necessary

Answer 1

You are given

 

T(x) = -22 + 46e^-0.03x

 

Initial temperature is at x = 0.

 

T(0) = -22 + 46e^-0.03(0) = -22 + 46 = 24°C

 

At 15 minutes,

 

T(15) = -22 + 46e^-0.03(15) ≅ 7°C

 

 

Answer 2

T(x)=-22+46e^-0.03x

 

Initial temperature is at zero minutes... T(0)

T(0) = -22 + 46e⁰ = -22 + 46 = 24 degrees

 

T(15) = -22 + 46e^-.03(15)

= -22 + 46e^-.45

= -22 + 46(.637628)

-22 + 29.331

= 7.331

≅ 7 degrees