The population of rabbits in an area is modeled by the growth equation p(t)=8e^0.26t, where P is in thousands and T is in years. How long will it take for the population to reach 25,000?

4.4

years corresponding to 4 years and 5 months (more or less)

Step-by-step explanation:

Let us set

P

=

25

we get:

25

=

8

e

0.26

t

rearrange:

e

0.26

t

=

25

8

take the natural log of both sides:

ln

[

e

0.26

t

]

=

ln

[

25

8

]

simplify:

0.26

t

=

ln

[

25

8

]

t

=

1

0.26

ln

[

25

8

]

=

4.38

≈

4.4

years corresponding to 4 years and 5 months (more or less)

I think you would times the exponents by each other and keep them in the parenthesis.