Mathematics: 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

its c. okay good luck on your homework okayStep-by-step explanation:...

At the start of the year, 15 chameleons were

Ответ:

7thaohstudent

10.03.2022

Mathematics

option-B

Step-by-step 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

$A_1=\frac{P(4)-P(2)}{4-2}$

now, we can plug values

$A_1=\frac{15(1.4142)^{4}-15(1.4142)^{2}}{4-2}$

A_1=14.99914

Average rate of change between 4 years and 6 years:

we can use formula

$A_2=\frac{P(6)-P(4)}{6-4}$

now, we can plug values

$A_2=\frac{15(1.4142)^{6}-15(1.4142)^{4}}{6-4}$

A_2=29.99770

Average rate of change between 6 years and 8 years:

we can use formula

$A_3=\frac{P(8)-P(6)}{8-6}$

now, we can plug values

$A_3=\frac{15(1.4142)^{8}-15(1.4142)^{6}}{8-6}$

A_3=59.99425

now, we will check each options

option-A:

we can see that

A_3-A_2=30

So, this is FALSE

option-B:

$A_1=\frac{1}{2}A_2$

So, this is TRUE

option-C:

This is FALSE

option-D:

we got

$A_1=\frac{1}{2}A_2$

so, this is FALSE

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