Question

(1 point) The fox population in a certain region has a relative growth rate of 8 percent per year. It is estimated that the population in the year 2000 was 9900. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). 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

this will be a exponential function as increase by percentage.

standard form of exponential function is

$\large P(t)=a*b^t$

here a is initial value of popupulatio. this means population when t=o . given t=0 means 2000 and population is 9900 .

so a=9900

b is growth factor . if growth rate percentage r is given then

b=1+ 100

so b here when growth rate is 8% is

$\large b=1+\frac{8}{100}=1.08$

so equation is

$\LARGE \boldsymbol{P(t)=9900*1.08^t}$

b)2008 means t=8 , apply this to equation and find population

$\large {P(8)=9900*1.08^8=18324.20908}\approx 18324$

so answer is 18324