# Suppose that the amount of algae in a pond doubles every 4 hours. If the pond initially contains...

## Question:

Suppose that the amount of algae in a pond doubles every 4 hours. If the pond initially contains 90 pounds of algae, how much algae will be in the pond after 12 hours?

A.) 720 pounds.

B.) 360 pounds.

C.) 1,440 pounds.

D.) 114 pounds.

## Exponential Growth:

An exponential growth process can describe population growth. Here, the growth of any number is exponential and not just linear. Exponential growth processes can vastly increase a quantity in a short amount of time.

At t = 0, we have 90 lb of algae. So at the first four hours, we should double this to get 180 lb. Now at the next four hour interval, the population doubles again. However, this time we will be doubling the current amount of algae, which is {eq}\displaystyle 180\ lb\times\ 2 = 360\ lb {/eq}. Now at the last four hour interval, we again double our current supply to get:

{eq}\displaystyle 360\ lb\ \times\ 2 = 720\ lb {/eq}

Therefore we have:

{eq}\displaystyle \boxed{(a) 720\ lb} {/eq} 