Question

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

Answer 1

Answer:

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

               $f(x)=250(0.88)^x$

Step-by-step 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

Answer:

The equation is equal to

$y=250(0.88^{x})$

Step-by-step 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

$y=250(0.88^{x})$