Question

An initial population of 7 chipmunks increases by 6% each year. If the function f(x) = abx models this situation, which function could you use to find the population after 8 years?

A) f(x) = 8(1.06)7
B) f(x) = 7(1.06)8
C) f(x) = 7(0.06)8
D) f(x) = 8(0.06)7

Answer 1

I’m not sure but i think it is a a

Answer 2

`f(x) = 7(1.06)^8`

Explanation:

Given : An initial population of 7 chipmunks increases by 6% each year.

To Find: which function could you use to find the population after 8 years?

Solution:

We are given that the function
`f(x) = ab^x` models this situation

Where a is the initial amount.

b = 1+r

r is the rate of change

x is number of years

Since we are given that initial population is 7

So, a = 7

We are also given that chipmunks increases by 6% each year.

So, r = 6%=0.06

So, b = 1+r = 1+0.06 = 1.06

Now we are supposed to find the function which can be used to find the population after 8 years

So, x =8

Substitute the values in the function:

`f(x) = 7(1.06)^8`

Thus Option B is correct .

Hence the function which represents the population after 8 years is
`f(x) = 7(1.06)^8`