College Algebra & Trigonometry, 2018a

3.1. EXPONENTIAL AND LOGISTIC APPLICATIONS 151
Example
The deer population on a nature preserve can be modeled using the equation:
y =
8000
1+9e −0.2t
y indicates the number of deer living in the nature preserve and t represents the
number of years that have passed since the initial population of deer were established
there.
a) How many deer were in the initial population?
b) What is the deer population after 10 years?
Round your answer to the nearest whole number.
c) How long does it take for the population to reach 5,000?
Round your answer to the nearest 10th of a year.
Parts (a) and (b) can both be answered from a table of values for the function.
Before we look at the table, let’s consider the question in Part (a). The problem is
asking what the initial population of deer was. The means that we’re looking to
find out what y is when t =0.
Let’s see what happens when we plug zero in for t in the formula:
y =
8000 8000
=
1+9e−0.2∗0 1+9e 0
= 8000
1+9∗ 1 = 8000
10
= 800