An experiment starts and the population of a bacteria culture increases by 10% in the first hour. Assume that the population increases at a rate proportional to the amount of bacteria.
a) What is the doubling time?
b) If the initial population is 2,000, what is the population in 6 hours?

a) The doubling time is 7.27 hours.

b) The population is 6 hours will be 3,543.

Step-by-step explanation:

The population of the bacteria is modeled by the following equation:

In which P(0) is the initial population, P(t) is the population after t hours and r is the growth rate.

An experiment starts and the population of a bacteria culture increases by 10% in the first hour.

This means that

Which helps us find r.

So

Applying ln to both sides

So

a) What is the doubling time?

This is t when

So

Applying ln to both sides

The doubling time is 7.27 hours.

b) If the initial population is 2,000, what is the population in 6 hours?

This is P(6) when . So

The population is 6 hours will be 3,543.

ratio is 2 : 9

the answer is three

13.5 : 3