Question

A culture started with 1,000 bacteria. After 3 hours, it grew to 1,100 bacteria. Predict how many bacteria will be present after 17 hours?

Answer 1

The general equation for exponential growth can be written as:

`x_(t) = x_(0) (1+r)^(t)`
where r is the growth rate.
Plugging in the given values, we get:

`1100=1000(1+r)^(3)`
Therefore

`(1+r)^(3)=1.1`
giving

`1+r= \sqrt[3]{1.1} =1.0323`
The predicted number of bacteria after 17 hours is given by:

`1000(1.0323)^(17)=1716`