Question: The number of diseased cells N(t) at time t increases at a rate of N'(t) = 60e^kt where k is constant. Calculate the value of the constant k if the rate of increase is 360 cells per day on the 5th day.

Using your value for k, determine the function N(t) if you have 100 diseased cells at time 0.

Calculate N(7), and explain the meaning of the answer in the context of this problem.