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%?

Oct 31, 2016

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

An exponential function is of the form of $y = A {\left(r\right)}^{x}$, where $A$ is the initial value and $r$ is the rate of increase/decrease in decimals.

The equation is hence $y = 430 {\left(0.86\right)}^{x}$. 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.

$P = 430 {\left(0.86\right)}^{t}$

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:

$P = 430 {\left(0.86\right)}^{5} = 202 \text{ animals}$

Hopefully this helps!