Question

A bacteria with an initial size of 180in2 grows by 27% every minute. What will the size of the bacteria be after 8hours

Answer 1

The size of the bacteria after 8 hours will be of
`1.2 * 10^(52)` squared inches.

Explanation:

Exponential function:

An exponential function has the following format:

`F(t) = F(0)(1+r)^(t)`

In which F(0) is the initial value and F is the growth rate.

A bacteria with an initial size of 180in2 grows by 27% every minute.

This means that
`F(0) = 180, r = 0.27`. So

`F(t) = F(0)(1+r)^(t)`

`F(t) = 180(1+0.27)^(t)`

`F(t) = 180(1.27)^(t)`

In which t is measured in minutes,

What will the size of the bacteria be after 8hours

8 hours has 8*60 = 480 minutes, so this is F(480).

`F(480) = 180(1.27)^(480) = 1.2 * 10^(52)`

The size of the bacteria after 8 hours will be of
`1.2 * 10^(52)` squared inches.