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 yearA. none of theseB. linearC. exponentialD. quadratic

Answer 1

Given the statement:

A population of wolves is presently at 500 and is decreasing by 10% each year.

Let's determine the type of model that best fits the given situation.

Here, given that the population of wolves decreases by 10% each year, the model that can be used to describe this situation is an exponential decay function.

A quantity can be siad to be subjected to an exponential decay if it decreases at a constant rate proportional to its current value.

To find the function apply the exponential decay function formula:

`f(x)=a(1-r)^x`

Where:

a is the current value = 500

r is the decay rate = 10% = 0.10

x is the number of years.

Hence, the exponential decay function that represents this situation is:

`\begin{gathered} f(x)=500(1-0.1)^x \\ \end{gathered}`

Therefore, the model that best fits the given situation is an exponential model.

ANSWER:

C. Exponential