Question

A culture of bacteria is growing at the rate of 20e^0.8t cells per day, where t is the number of days since the culture was started. Suppose that the culture began with 50 cells.
(a) Find a formula for the total number of cells in the culture after t days.
(b) If the culture is to be stopped when the population reaches 700, when will this occur? (Round your answer to one decimal place.)

Answer 1

If N is the number of bacteria

dN/dt = 20e^.8t
N = 25 e^.8t + 50

when N = 700
700 = 25 e^.8t + 50
e^.8t = 26
take ln of both sides
.8t = ln 26
t = appr 4.07

check:
if t = 4.07
N = 25 e^.8(4.07) + 50
= 698.6 , not bad