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.

Solution:

a) If there is an increase in the population by 11%, it should be multiplied by 1.11 each year. By raising 1.11 to the number of years will determine the increase in population.

Now multiplying the number with the original population will help us to determine the total population as an exponential function.

y = 330 × 1.11ⁿ

b) y represents the population after n years

n is the number of years

c) We have to find the number after 5 years

y = 330 × 1.11⁵

y = 330 × 1.685

y = 556.05

Therefore, the exponential function is y = 330 × 1.11n, y represents the population after n years n is the number of years, and y = 556.05 after 5 years.

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.

Summary:

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) An exponential function to model the deer population in terms of the number of years from now is y = 330 × 1.11n.
b) The value in the model represents y represents the population after n years n is the number of years.
c) The number of deer that will be in the region after five years is 556.05