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%?

1 Answer
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(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!