precalc question

Question

A cancerous cell lacks normal biological growth regulation and can divide continuously. Suppose a single mouse skin cell is cancerous and its mitotic cell cycle (the time for the cell to divide once) is 20 hours. The number of cells at time t grows according to an exponential model.

(a) Find a formula C(t) for the number of cancerous skin cells after t hours.

(b) Assume a typical mouse skin cell is spherical of radius 50×10^(−4) cm. Find the combined volume of all cancerous skin cells after t hours. When will the volume of cancerous cells be 1 cm^3?

Answer 1

(a)

C(t) = 1(2)^t/20

(b)

V(t) = (4/3)π(50 x 10^-4)³(2)^t/20