Question

4. An initial population of 825 quail increases at an

annual rate of 13%. Write an exponential
function to model the quail population in 3
years.
A. Y = 825(1.13)^3
B. Y = 8250(.87)^3
C. Y = 825(13)3^3
D. Y = 825(87)3^3

Answer 1

A

Explanation:

The general form of compound growth formula is:

`F=P(1+r)^t`

Where

F is the future amount

P is the initial amount

r is the rate of growth in decimal

t is the time in years

In the problem, initially there is 825 quail, so

P = 825

The future amount is given as "Y", so we will replace "F" of formula by "Y"

The rate of growth in 13%. This converted to decimal is:

13/100 = 0.13

The time is 3 years, so t = 3

Now, we substitute and find the model equation:

`F=P(1+r)^t\\Y=825(1+0.13)^3\\Y=825(1.13)^3`

Correct answer choice is A