# Under ideal conditions, a population of rabbits has an exponential growth rate of 11.5% per day. Consider an initial population of 900 rabbits, how do you find the growth function?

Apr 4, 2018

$f \left(x\right) = 900 {\left(1.115\right)}^{x}$

#### Explanation:

The exponential growth function here takes on the form

$y = a \left({b}^{x}\right) , b > 1 , a$ represents the initial value, $b$ represents the rate of growth, $x$ is time elapsed in days.

In this case, we're given an initial value of $a = 900.$

Furthermore, we're told that the daily growth rate is 11.5%.

Well, at equilibrium, the growth rate is zero percent, IE, the population remains unchanged at 100%.

In this case, however, the population grows by 11.5% from equilibrium to (100+11.5)%, or 111.5%

Rewritten as a decimal, this yields $1.115$

So, $b = 1.115 > 1$, and

$f \left(x\right) = 900 {\left(1.115\right)}^{x}$