Calculus Question - See Description

Question

Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of T and the temperature of the region, T_R or  An object with core temperature of 1200°F is removed from a fire and placed in a region with a constant temperature of 80°F. After 1 hour, its core temperature is 830°F. What is the object's core temperature 4 hours after it is taken off the fire?

 

a) 370.4010°F

b) 305.2214°F

c) 225.2214°F

d) 145.4010°F

Answer 1

This is a 1st order linear equation with solution T=T_R + Ce^-kt

and you use the initial conditions to find the values of C and k

Clearly C=1120.and you should be able to do the rest.

Oh, the DE:

e^-kt is an integrating factor, i.e.

T'e^-kt - Tke^-kt = -kT_Re^-kt

and the solution is Te^-kt = ∫-kT_Re^-kt dt