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Nataliya [291]
3 years ago
5

At the start of the year, 15 chameleons were introduced into a zoo. The population of chameleons is expected to grow at a rate o

f 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.
Mathematics
1 answer:
bearhunter [10]3 years ago
5 0

Answer:

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

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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