Under certain conditions, the number of cancer cells N(t) at time t increases at a rate N′(t) = Ae^kt, where A is the rate of increase at time 0 (in cells per day) and k is a constant.
(a) Suppose A = 50, and at 5 days, the cells are growing at a rate of 250 per day. Find a formula for the number of cells after t days, given that 300 cells are present at t = 0.
(b) Use your answer from part (a) to find the number of cells present after 12 days.