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%. Write an exponential function to model the deer population. Explain what each value in the model represents. Predict the number of deer that will be in the region after five years. Show your work.

Answer 1

Answer: p = 330 × (1.11)^n;p = population after n years n = number of years; 556

Step-by-step explanation:

Current population = 330

Increment percentage = 11% per annum

Increment = 11÷100 = 0.11

Therefore, each year, deer population rises by 0.11, 1+0.11 = 1.11

For instance,after one year, 330 ×(1.11)^1

A. Therefore, Exponential function to model Increment after n years is given by;

Population after n years is given by ;

p = 330 × (1.11)^n

B. Parameter definition;

p = population after n years

n = number of years

C. Population of deer after five years using the model

p =

n = 5

p = 330 ×(1.11)^5

p = 330 × 1.685

p = 556.05

Therefore, deer population after five years is approximately 556 as derived from the model.

Answer 2

Answer: If the population is increasing by 11%, the poplation is being multiplied by 1.11 annually. Raising 1.11 to the amount of years would offer you what proportion the population increases. Multiplying this number by the first population will offer you the entire population.

A. Exponential function to model the deer population;

y = 330 * (1.11)^n

B. Each value in the model represents.

y = population after n years

n = number of years

C. The number of deer that will be in the region after five years.

y = 330 * (1.11)^n

y = 330 * (1.11)^5

y = 330 * 1.685

y = 556.05

There will be 556 deer after 5 years based on the model.