Exponential Problem?

Question

A bacteria cell divides into two cells every 20 minutes. The initial population of a culture is 60 cells.
a. find the relative growthing rate
d. find an expression for the # of cells after t hrs
c. find the rate of growth after 8hrs
d. when will the population reach 20,000 cells?

Answer 1

B = k e^at t in hours
For t= 0 60= k and for t =1/3 B=120
so
120 = 60*e^a/3 so a/3 = ln 2 and a = 3 ln 2
B = 60 e^3ln 2*t =60 * 8^t (cells after t hours)
dB/dt =60*8^t*ln8 and at t=8 = 60*8^8*ln8 cells/h
20,000 =60 *8^t
ln (2000/6)= t*ln8 so t=2.8 h