Question

How do you write an exponential function to model the situation. then predict the value of the function after 5 years (to the nearest whole number). A population of 430 animals that decreases at an annual rate of 12%?

Answer 1

If the rate of decrease is `-0.12`, and this can be written as `0.86`.

An exponential function is of the form of `y = A(r)^x`, where `A` is the initial value and `r` is the rate of increase/decrease in decimals.

The equation is hence `y = 430(0.86)^x`. However, let's use some variables that are a little more descriptive. Let's use `P` for population as the dependant variable, dependant on `t`, or time, in years.

`P = 430(0.86)^t`

Now, the problem asks us to find the number of animals after `5` years. We simply substitute `t = 5` into the function, and that will give us:

`P = 430(0.86)^5 = 202" animals"`

Hopefully this helps!