The doubling period of a baterial population is

20
20
minutes. At time
t
=
80
t=80
minutes, the baterial population was 50000.

What was the initial population at time
t
=
0
t=0
?

80 is 4 half-lives, so at t=0, it was 16 (2^4) times as great.

To find the initial population at time t=0, we need to use the doubling period and the population at a later time.

The doubling period refers to the time it takes for the population to double in size. In this case, the doubling period is given as 20 minutes.

Since we know that the population doubled in size every 20 minutes, we can calculate the number of doubling periods that have passed from t=0 to t=80 minutes.

Number of doubling periods = (time elapsed)/(doubling period) = 80/20 = 4 doubling periods.

Now, we need to calculate the population at time t=0 using the population at t=80 minutes and the number of doubling periods.

The formula to calculate the initial population from a known population and the number of doubling periods is:

Initial population = (known population) / (2^number of doubling periods)

Plugging in the values, we have:

Initial population = 50000 / (2^4) = 50000 / 16 = 3125

Therefore, the initial population at time t=0 is 3125.