calculus rates problems! need help?

Question

Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees Farenheit during the first hour after death and about 1 degrees Farenheit for each additional hour. Assuming an air temperature of 68 degrees F and a living body temperature of 98.6 degrees F, the temperature T(t) in F of a body at a time t hours since death is given by

T(t) = 68 + 30.6e^(-kt)

For what value of k will the body cool by 2 F in the first hour

question b.

using the value of k found in part a, after how many hours will the temperature of the body be decreasing at a rate of 1F per hour?

Answer 1

Well, you know that T(0) = 98.6 and T(1) = 96.6. Considering T(1), we have
96.6 = 68 + 30.6e^(-k)
28.6 = 30.6/(e^k); remember that raising to a negative is the same as dividing by the positive power
28.6e^k = 30.6
e^k = 1.0699
k = ln 1.0699 = .0676