Answer:
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
