Question

Which equation represents a population of 250 animals that decreases at an annual rate of 12%​

Answer 1

The equation which represents a population of 250 animals that decreases at an annual rate of 12%​ is:

`f(x)=250(0.88)^x`

Explanation:

It is given that:

A population of 250 animals decreases at an annual rate of 12%​.

This problem could be modeled with the help of a exponential function.

`f(x)=ab^x`

where a is the initial amount.

and b is the change in the population and is given by:

`b=1-r` if the population is decreasing at a rate r.

and
`b=1+r` if the population is increasing at a rate r.

Here we have:

`a=250`

and x represents the number of year.

`r=12\%=0.12`

Hence, we have:

`b=1-0.12=0.88`

Hence, the population function f(x) is given by:

`f(x)=250(0.88)^x`

Answer 2

The equation is equal to

`y=250(0.88^(x))`

Explanation:

we know that

In this problem we have a exponential function of the form

`y=a(b^(x))`

where

x -----> the time in years

y ----> the population of animals

a is the initial value

b is the base

r is the rate of decreasing

b=(1-r) ----> because is a decrease rate

we have

`a=250\ animals`

`r=12\%=12/100=0.12`

`b=(1-0.12)=0.88`

substitute

`y=250(0.88^(x))`