Question

Researchers recorded that a group of bacteria grew from 200 to 1,000 in 8 hours. At this rate of growth, how many bacteria will there be in 20 hours from the start of the experiment

Answer 1

11,180

Explanation:

The usual assumption for organic growth is that it is exponential. Here, the number increased by a factor of 1000/200 = 5 in 8 hours. For t in hours, a model for population might be ...

b = (initial value)·(growth factor)^(t/(period of growth))

b = 200(5^(t/8))

Using t = 20, the predicted population is ...

b = 200(5^(20/8)) = 200·5^2.5 ≈ 11,180

There might be about 11,180 bacteria in 20 hours.