Question

At the start of the year, 15 chameleons were introduced into a zoo. The population of chameleons is expected to grow at a rate of 41.42% every year. The function below models the population of chameleons in the zoo, where x represents the number of years since the chameleons were introduced into the zoo.

A. The average rate of change in the population between year 4 and year 6 was 41 more than the average rate of change in the population between year 6 and year 8.
B. The average rate of change in the population between year 2 and year 4 was approximately half the average rate of change in the population between year 4 and year 6. C. The average rate of change in the population between year 4 and year 6 was the same as the average rate of change in the population between year 6 and year 8. D. The average rate of change in the population between year 2 and year 4 was approximately double the average rate of change in the population between year 4 and year 6.

Answer 1

did u ever find an answer to this question?

Explanation:

Answer 2

option-B

Explanation:

We are given

At the start of the year, 15 chameleons were introduced into a zoo

so,
`P_0=15`

The population of chameleons is expected to grow at a rate of 41.42% every year

so, r=0.4142

and x represents the number of years since the chameleons were introduced into the zoo

now, we can set equation to find total population

and we get

`P(x)=P_0(1+r)^x`

now, we can plug values

`P(x)=15(1+0.4142)^x`

`P(x)=15(1.4142)^x`

Average rate of change between 2 years and 4 years:

we can use formula

`A_1=(P(4)-P(2))/(4-2)`

now, we can plug values

`A_1=(15(1.4142)^(4)-15(1.4142)^(2))/(4-2)`

`A_1=14.99914`

Average rate of change between 4 years and 6 years:

we can use formula

`A_2=(P(6)-P(4))/(6-4)`

now, we can plug values

`A_2=(15(1.4142)^(6)-15(1.4142)^(4))/(6-4)`

`A_2=29.99770`

Average rate of change between 6 years and 8 years:

we can use formula

`A_3=(P(8)-P(6))/(8-6)`

now, we can plug values

`A_3=(15(1.4142)^(8)-15(1.4142)^(6))/(8-6)`

`A_3=59.99425`

now, we will check each options

option-A:

we can see that

`A_3-A_2=30`

`A_3-A_2=30`

So, this is FALSE

option-B:

`A_1=(1)/(2)A_2`

So, this is TRUE

option-C:

This is FALSE

option-D:

we got

`A_1=(1)/(2)A_2`

so, this is FALSE