Question

Determine what type of model best fits the given situation a population of wolves is presently at 500 and is decreasing by 10% each year.

A. Quadratic
B. Exponential
C. Linear
D. None of these

Answer 1

Option: B is the correct answer.

B. Exponential

Explanation:

We know that a exponential function is given by:

`f(x)=a(1\pm r)^x`

where a is the initial value of the function.

and r is the rate of increase or decrease.

if r decreases then we have the total change as: 1-r

and if r increases then we have the total change as: 1+r

Here r=10%=0.10

a= 500

Hence, we have:

the population function f(t) over the time t years is given by:

`f(t)=500(1-0.10)^t\\\\f(t)=500(0.90)^t`

Hence, the model that best fits the given situation is: Exponential.

Answer 2

B. Exponential

Explanation:

The annual wolf population in each year is

w = 500 500(0.9) 500(0.9)² 500(0.9)³ …

n = 1 2 3 4 …

The model is w = 500(0.9)ⁿ⁻¹.

This is an exponential model, because the independent variable is in an exponent.