Question

The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 19100.
(a) Find a function that models the population t years after 2000(t=0 for 2000).
Hint: Use an exponential function with base e.
Your answer is P(t)=

(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)

Answer 1

Answer

a)

$P(t) = 19100. e^{0.06t}$

b) P(8) =30866

Step-by-step explanation

Use formula:

$P(t) = P. e^{rt}$

a)

Here, P = 19100

r = 6% = 0.06

$P(t) = 19100. e^{0.06t}$

b) t = 2008 - 2000 = 8

$P(8) = 19100. e^{0.06\times 8}$

$P(8) = 19100. e^{0.48}$

$P(8) = 19100\times 1.616\\\\P(8) = 30,865.6\\\\P(8) \approx 30,866$