The Law of Exponential Growth

Question

Please help me understand this with the formulas needed.

 

The fox population in a certain region has a relative growth rate of 5% per year. It is estimated that the population in the year 2000 was 10500.

 

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

P(t)=

 

b. use the function from part a to estimate the fox population in the year 2008. (answer much be an integer)

Answer 1

Use the formula

 

P(t) = P₀e^kt

 

where:

P(t) = population

P_o = initial population

k = growth factor (in decimal)

t = time in years (t=0 for 2000)

 

The formula we want using the given information is

 

P(t) = 10500e^0.05t

 

 

Now just use the formula to answer part b.