The doubling period of a bacterial population is 20 minutes

The doubling period of a bacterial population is 20 minutes. At time t=90 minutes, the bacterial population was 9000. What was the initial population at time t=0? Find the size of the bacterial population after 5 hours.

Solution

Equation of bacterial growth : N = Noe^kt

doubling period of a bacterial population is 20 minutes:

2No = Noe^(20k)

2 = e^20k

take log on both sides:

ln2 = 20k

k =0.693/20 =0.0347

At time t=90 minutes, the bacterial population was 9000 : find No (intial amount)

9000 = Noe^(0.0347*90)

No = 9000/22.71 = 396.30

Size of population after 5 hrs = 300min: N = 396e^(0.0347*300) = 13143188.52 = 13143189