Calculus 2 Rates - Newton's Law of Cooling

Question

(1 point) Newton's Law of Cooling states that the rate at which an object cools is proportional to the difference in temperature between the object and the surrounding medium. Thus, if an object is taken from an oven at 290∘F and left to cool in a room at 80∘F, its temperature T after t hours will satisfy the differential equation:

 

dT/dt=k(T−80).

 

If the temperature fell to 190∘F in 0.7 hour(s), what will it be after 3 hour(s)?

Answer 1

This is a separable differential equation.

 

dT/dt = k(T-80)

 

move dt to fight and divide by T-80

 

dT/(T-80) = kdt

integrate

 

ln|T-80| = kt + C

 

you are given temp is 190 at t= 0.7. And temp at t = 0 is 290. 

so t = 0

ln(210) = C

t = 0.7

ln(110) = 0.7k+ln210 

so k = ln(110/210)/0.7

 

now plug in t = 3.

hope helpful 

Beat - david