Help with Decay Problem?

Question

According to Newton's Law of Cooling, if a body with temperature T in base 1 is placed in surroundings with temperature T in base 0, different from that of T in base 1, the body will either cool or warm to temperature T(t) after t minutes, where T(t) = T in base 0 + (T in base 1 - T in base 0)e^kt

A cup of coffee with temperature 125 degrees (F) is placed in a freezer wither temperature of 0 degrees (F). After 15 minutes, the temperature of the coffee is 37 degrees (F). Use Newton's Law of Cooling to find the coffee's temperature after 20 minutes.

Answer 1

Since the "reservoir" temperature is 0,

125e^15k = 37

15k = Ln(37/125)

k = (1/15)Ln(37/125) ≈ - 0.0811597216/min.

T = 125e^[(20 min.)(- 0.0811597216 /min.)

T ≈ 24.7°F

Since this is probably below the freezing point of coffee, the temperature will have stabilized at the freezing point of coffee.