Answer:
(a) P(x) = Pi*(1+r)^x (terms defined below. x is years since 2000)
(b) 15733 fox population
Explanation:
(a) Let P stand for the population and Pi is the initial fox population. Let x be the number of years that the fox population is growing at rate r (percent per year).
The relationship between population and growth rate can be written as:
P(x) = Pi*(1+r)^x
This is telling us that the fox population x years after the initial population (Pi) will be (1+r) taken to the power of the years the population is growing.
(b) The fox population is 2008 is forecast to be 15733.
Year Population Rate(r) Years Since Calculation Result
2000 8500 0.08 0 8500*(1.08)^0 8500
2001 1 8500*(1.08)^1 9180
2002 2 8500*(1.08)^2 9914
2008 8 8500*(1.08)^8 15733
The initial population, Pi, is 8500 for year 2000.
The growth rate, 0.08 or 8%, is added to 1, since 1 represents the population at the start of that year. That results in the factor (1 + 0.8)
If using an Excel spreadsheet, the cell formula would be = 8500*(1+0.08)^(year - 2000).
P(2008) = (8500)*(1.08)^(2008-2000)
P(2008) = (8500)*(1.08)^8
It can be seen that the resulting population in 2008 is simply the initial population time the growth factor of 1.08 raised to the number of years the growth occurs after 2000.
(8500)*(1.08)*(1.08)*(1.08)*(1.08)*(1.08)*(1.08)*(1.08)*(1.08) which is (1.08) times itself for the 8 years of growth.