A loaf of bread is removed from an oven at 350° F and cooled in a room whose temperature is 70° F. If the bread cools to 210° F in 20 minutes, how much longer will it take the bread to cool to 185° F.

The bread will take 216.40 minutes to cool to 185°F

Explanation: Newton law of cooling

states that the rate of cooling of an object is inversely proportional to the difference of temperatures between the object and its surroundings i. e. dTdt=-kT, where t is the time taken and T is the difference of the temperatures between the object and its surroundings.

This gives us T as a function of t and is given by T (t) = ce-kt.

T (0) = Ce^-kt

C=35₩F - 185F = 165F

T (20) = 165*e^-20k = (350-70)

T (20) = e^-20k = 280/165

-20k = ln (280/165)

-20k = ln (1.697)

-20k = 0.5289

K = 0.5289/20

K = 0.0264

If it cools at 185F in t minutes

165e^-0.0264*t=0.5

e^-0.0264t = 0.5/165

-0.0264t = on 3.03*10^-3

-0.0264t = - 5.7129

t = 5.7129/0.0264

t=216.40minutes