Question

The fox population in a certain region has a relative growth rate of 4% per year. It is estimated that the population in year 2000 was 17900.(A.) Find a function that models the population t years after 2000 (t=0 for 2000) and (B.) Use the function from part A to estimate the fox population in the year 2008.------> answer must be an integer.

Answer 1

Answer:

a) $P(t) = 17900e^{0.04t}$

b) The population estimated in 2008 is of 24651.

Step-by-step explanation:

The population growth model may be given by the following exponential function:

$P(t) = P_{0}e^{rt}$

In which P(t) is the population after t years, $P_{0}$ is the initial population and r is the growth rate.

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

We have that:

$P_{0} = 17900, r = 0.04$. So

$P(t) = P_{0}e^{rt}$

$P(t) = 17900e^{0.04t}$

(B.) Use the function from part A to estimate the fox population in the year 2008.

2008 is 8 years after 2000. So:

$P(8) = 17900e^{0.04*8} = 24650.5$

The population estimated in 2008 is of 24651.