# Suppose in January, t=1 , a lake is covered by 2 square meters of algae. Every month, the area...

## Question:

Suppose in January, {eq}t=1 {/eq} , a lake is covered by {eq}2m^2 {/eq} of algae. Every month, the area covered by algae doubles. (Assume that the growth occurs continuously.) Find the growth rate as a function of time with units square meters per month.

## Exponential Growth

A quantity can grow in a variety of ways. If we are given this growth in terms of doubling time, this growth takes an exponential form. The function that describes this growth can be written as follows.

{eq}f(t) = C\cdot 2^{\frac{t}{d}} {/eq}

Since the population doubles every month, we can write an exponential function that defines this growth. The initial value of 2 square meters is the coefficient in front of the exponential base, and the doubling time of 1 month is included in the exponent. Specifically, we divide our variable by 1. Therefore this function has the form below.

{eq}f(t) = 2\cdot 2^{\frac{t}{1}} = 2 \cdot 2^t {/eq} 