Question

In a particular region of a national park, there are currently 330 deer, and the population is increasing at an annual rate of 11%.
a. Write an exponential function to model the deer population in terms of the number of years from now.
b. Explain what each value in the model represents.
c. Predict the number of deer that will be in the region after five years. Show your work.

Answer 1

Answer:

a) P(t) = 330 $(1.11)^{t}$

b)P(t) →population after t years.

   t →number of years.

c) Number of deer after five years = 556

Step-by-step explanation:

a) The population increasing at an annual rate of 11%, means the population is being multiplied by 1.11 each year.

So, we can use the formula

                             P(t) = P $(1+\frac{r}{100} )^{t}$

                             P(t) = 330 $(1+\frac{11}{100} )^{t}$

                             P(t) = 330 $(1.11)^{t}$

b) In this model

                        P(t) → population after t years

                          P → present population

                          r → annual increasing rate

c) Number of population after 5 years is,

                    P(5) = 330 $(1.11)^{5}$

                           = 556

 Number of deer after 5 years = 556