Question

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?

Answer 1

`f(x)=900(1.115)^x`

Explanation:

The exponential growth function here takes on the form

`y=a(b^x), 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(x)=900(1.115)^x`