Exponential Growth/Decay

Question

A bottle of seltzer water initially has a temperature of 79°F. It is left to cool in a refrigerator that has a

temperature of 38°F. After 10 minutes the temperature of the seltzer water is 66°F. Use​ Newton's Law of​ Cooling, T=C+(T0−C)e^kt​, to find a model for the temperature of the seltzer water​, ​T, after t minutes.

Answer 1

79 at time t=0

38 = temp in refrigerator

10 min=1/6 hr goes to 66 degrees

T(1/6) = 38 + (79-38)e^k/6=66

41e^k/6 = 66-38=28

e^k/6= 28/41

k=6ln(28/41)

T(t) = 38 +41e^tln(28/41)

Answer 2

Solved, with (hopefuly!) sufficient detail and explanation.