math question please help

Question

A hot coffee just brewed(180F) from the coffee machine is placed in a room where the temperature is 65F. After 20 minutes, the hot coffee has cooled to 140F. Find the temperature after one hour 06 minutes.

On my study guide, it says the answer is 112.6F, but I keep getting 93.06F. Can someone please explain what I'm doing wrong? Thank you!

Answer 1

This is Newton law of cooling. In our case:

T(t) = 65 + (180 - 65)e^-rt; T(t) = 65 + 115e^-rt;

T(20) = 65 + 115e^-20r = 140; e^-20r = 75/115 = 15/23; r = ln(15/23)/(-20) = 0.02137

T(60) = 65 + 115e^-0.02137·66 = 93.06° F