A cup of coffee at 90 degrees Celsius is put into a 15 degree Celsius room when t=0. The coffee's temperature, f(t), is changing at a rate given by f′(t)=−8(0.6)^t degrees Celsius per minute, where t is in minutes.
Estimate the coffee's temperature when t=12:
f'(t) = -8(0.6)^t
f(t) = -8/ln0.6 (0.6)^t + C
since f(0) = 90,
-8/ln0.6 + C = 90
f(t) = 15.66(0.6)^t + 74.34
Now use that C and find f(12)