Question

The fox population in a certain region has a continuous growth rate of 5% per year. It is estimated that the population in the year 2000 was 10,100 foxes.

a) Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).
b) Use your function from part (a) to estimate the fox population in the year 2008.
c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.

Answer 1

P(t) = I × ( 1 +g)^t

14922

2013

Explanation:

Given the following :

Growth rate (g) = 5% = 0.05

Initial population (I) = 10,100

Time (t) = t (t = 0 in year 2000)

A) population function P(t)

P(t) = I × ( 1 +g)^t

P(t) population in t years

I = inital population

g = growth rate

t = years after year 2000

B) Population Estimate in year 2008

2008 - 2000 = 8 = t

P(8) = 10,100 × ( 1 +0.05)^8

P(8) = 10,100 × (1.05)^8

P(8) = 10,100 × 1.4774554437

P(8) = 14922.299 = 14922

C.) Nearest whole year when population will reach over 18,400

18,400 = 10,100 × ( 1 +0.05)^t

18400 = 10,100(1.05)^t

1.05^t = 18400 / 10,100

1.05^t = 1.8217821

In(1.05^t) = ln(1.8217821)

(0.0487901)t = 0.5998152

t = 0.5998152 / 0.0487901

t = 12.293789

To attain a population of 18400 and over, the nearest whole year = 13 years

2000 + 13 = 2013