A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.

B) Find general solution by separating variables and integrating

:
C) Initial condition is t=0, T = 87

D) Total time elapsed is 10 minutes, new temperature is 84

solve for alpha

E) Temperature function is:

solving for t

Plug in T = 98.6

This is approximately 32 minutes before he arrived or about 1:20 AM
The answer is 9 because 25% of 60 is 15 plus 60% of 60 is 36 so 36+15=51 and 60-51=9
True, but not many. Insurance companies typically have a cap off so the client doesn't go in let's say every week for a check up to see if they grew an inch. This is form personal experience in reading into the fine print.
1/4 : 2 or 1/8 : 1. That is how I would have done it. I hope this helps you.