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.

option-B

Step-by-step explanation:

We are given

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

so,

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

now, we can plug values

Average rate of change between 2 years and 4 years:

we can use formula

now, we can plug values

Average rate of change between 4 years and 6 years:

we can use formula

now, we can plug values

Average rate of change between 6 years and 8 years:

we can use formula

now, we can plug values

now, we will check each options

option-A:

we can see that

So, this is FALSE

option-B:

So, this is TRUE

option-C:

This is FALSE

option-D:

we got

so, this is FALSE

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3