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 is:
P(t) = 330 * 1.11^t
Where:
P(t) is the population of deer after t years
330 is the initial population of deer
1.11 is the growth rate, which is equivalent to 11%
t is the number of years from now
b. In the exponential function:
- The initial population of deer (330) represents the starting point of the population before any growth.
- The growth rate (1.11) represents the percentage increase in the population each year.
- The variable t represents the number of years from now that we are predicting the population.
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 * 1.11^5
P(5) = 330 * 1.629
P(5) ≈ 537.57
Therefore, after five years, it is predicted that there will be approximately 538 deer in the region of the national park.