Question

The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 21400.

(a) Find a function that models the population
t
years after 2000 (
t
=
0
for 2000

Answer 1

Explanation:

Let P(t) be the fox population t years after 2000. We know that the population has a continuous growth rate of 4% per year, which means that the population increases by a factor of 1.04 each year. Therefore, we can model the population as:

P(t) = 21400 * 1.04^t

Here, we start with the population in the year 2000 (21400) and multiply it by 1.04 raised to the power of the number of years after 2000 (t).

For example, if we want to find the population in the year 2015 (15 years after 2000), we can plug t = 15 into the equation:

P(15) = 21400 * 1.04^15

= 21400 * 1.618

= 34694.8

Therefore, we can expect the fox population to be approximately 34,695 in the year 2015.