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

Answer:

Option: B is the correct answer.

         B.   Exponential

Step-by-step 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

Answer:

B. Exponential

Step-by-step 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.