Question

The doubling period of a bacterial population is 15 minutes. At time t=120 minutes, the bacterial population was 60000.A) What was the initial population at time t=0?B) Find the size of the bacterial population after 3 hours

Answer 1

If you follow the formula

$y=ab^t$

Where y is the total amount of bacteria, a is the initial bacterial at time 0, and b is the growth factor.

A) At t=120 minutes. This would be 15 minutes 8 times. So the time for t=8:

$\begin{gathered} 60000=a(2)^8 \\ 60000=a(256) \\ \frac{60000}{256}=\frac{a(256)}{256} \\ a=234.375 \end{gathered}$

Answer a: the initial population = 234.375

B) The equation is given by:

$y=234.375(2)^t$

After 3 hours (15 minutes, 12 times), or at t = 12 you would get:

$y=234.375(2)^{12}=960000$

Answer b: the bacterial population = 960000