Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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.
a. The exponential function to model the deer population in terms of the number of years from now can be written as:
P(t) = P0 * (1 + r)^t
Where:
P(t) represents the deer population after t years.
P0 represents the initial population, which is 330 deer.
r represents the annual growth rate converted into decimal form. In this case, it is 11% or 0.11.
t represents the number of years from now.
b. Each value in the model represents the following:
P(t) represents the deer population after t years.
P0 represents the initial population, which is 330 deer.
r represents the annual growth rate converted into decimal form. In this case, it is 11% or 0.11.
t represents the number of years from now.
c. To predict the number of deer that will be in the region after five years, we substitute t = 5 into the exponential function:
P(5) = 330 * (1 + 0.11)^5
P(5) = 330 * (1.11)^5
P(5) = 330 * 1.6755
P(5) ≈ 552.715
Therefore, the predicted number of deer in the region after five years is approximately 552.715.