Question

The number of bacteria present in a colony is 180 at noon and the bacteria grows at a rate of 22% per hour. How many will be present at 8 p.M.? Round to the nearest whole bacteria.

Answer 1

883 bacteria

Explanation:

The number of bacteria at noon (12:00 pm) is 180. It increases at a rate of 22% every hour.

At 08:00 pm, 8 hours will have elapsed.

This is a compound interest problem. The final amount of bacteria will be:

`B = P(1 + r)^t`

where P = initial amount of bacteria = 180

r = rate of increase = 22% = 0.22

t = time elapsed = 8 hours

Therefore:

`B = 180(1 + 0.22)^8\\\\B = 180 (1.22)^8\\\\B = 180 * 4.908`

`B = 883.44` ≅
`883`

There will be 883 bacteria by 8 PM.