Question

There is a population of 500 bacteria in a colony. If the number of bacteria doubles every 260 minutes, what will the population be 520 minutes from now?

Answer 1

From the statement of the problem, we know that:

• the initial population of bacteria in a colony is N_0 = 500,

,

• the number of bacteria doubles every △t = 260 min.

We can model the population of bacterias in the colony by the exponential function:

`N(t)=N_0\cdot r^(t/\Delta t)=500\cdot2^(t/260\min .)`

After a time t = 520 min, the population will be:

`N(520\min )=500\cdot2^(520\min /260\min )=500\cdot2^2=500\cdot4=2000.`

Answer

After 520 minutes, the population will be 2000 bacterias.