The united states population of gray wolves was 1170 in 1991. if the population is decreasing by 5% each year, how long before there are only 300 left?

27 years.

Step-by-step explanation:

We have been given that the United States population of gray wolves was 1170 in 1991. The population is decreasing by 5% each year.

We can see that population of grey wolves is decreasing exponentially, so we will use an exponential function to model the population after x years.

Since we know that exponential function is in form: , where,

a = Initial value,

b = For decay b is in form (1-r), where r represents decay rate in decimal form.

Let us convert our given decay rate in decimal form.

Upon substituting our given values we will get our function as:

, where x represents number of years.

To find the time it will take the population to reach 300 we will substitute y=300 in our function.

Let us divide both sides of our equation by 1170.

Let us take natural log of both sides of our equation.

Using natural log property we will get,

Therefore, it will take approximately 27 years to the population of grey wolves to reach 300.

1

step-by-step explanation:

it's the only multiple of both and the least

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).