Need some help with a hard question
Ok the question is
Coroners estimate the time of death from body temperature using the simple rule that a body cools about 1C in the first hour after death and about 1/2C for each addictional hour.
Assuming an air temperature of 20C and a living body temperature of 37C, the temperature, T(t), in degrees Celcius is given by T(t) = 20 + 17e^-kt, where t=0 is the instant that death occurred..
a) For what value of k will the body cool by 1C in the first hour?
b) Using the value of k found in part a) after how many hours will the temperature of the body be decreaing at a rate of 1/2 C per hour?
c) Using the value of k found in part a) Show that 24h after death, the coroner's rule gives approx the same temp as the forumula.
I know I need an equation to do this but Im not sure what it is, I understood my other log study questions but this one stumps me. Any help would be appreciated greatly.