Under certain conditions, the number of diseased 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 = 40, and at 3 days, the cells are growing at a rate of 160 per day. Find a formula for the number of cells after t days, given that 200 cells are present at t = 0.
b. Use your answer from part a to find the number of cells present after 7 days.
a. Find a formula for the number of cells, N(t), after t days.
N(t) = 86.6 e^{0.46210t} + 113.4
(Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.)
b. After 7 days, there are 2,313 cells present.
(Use the answer from part a to find this answer. Round to the nearest whole number as needed.)
