The exponential function involving doubling period is expressed as
P = Po(2)^t/T
where
Po is the initial or starting value
t is the time of growth
T is the doubing time
t/T is the ratio describing the number of doubings over time t
From the information given,
T = 15
t = 80
P = 80000
We want to find Po
We have
80000 = Po(2)^80/15
80000 = 40.32Po
Po = 80000/40.32 = 1984
The initial population is 1984
Thus, the function is
P = 1984(2)^t/15
For 3 hours, recall,
1 hour = 60 minutes
3 hours = 3 * 60 = 180 minutes
We would substitute t = 180 into the equation. We have
P = 1984(2)^180/15 = 1984(2)^12
P = 8126464
The size of the bacterial population after 3 hours is 8126464
