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The function f(x)=1200(1.055)x models the balance of an investment x years after it is made.

How does the average rate of change between years 21 and 25 compare to the average rate of change between years 1 and 5?

The function fx12001055x models the balance of an investment x years after it is made How does the average rate of change between years 21 and 25 compare to the class=

Respuesta :

Answer:

option-B

Step-by-step explanation:

We are given function as

[tex]f(x)=1200(1.055)^x[/tex]

Average rate of change between 21 and 25 years:

we can use formula

[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]

so, we have

a=21 and b=25

[tex]f(21)=1200(1.055)^{21}=3693.88[/tex]

[tex]f(25)=1200(1.055)^{25}=4576.0708[/tex]

[tex]A=\frac{f(25)-f(21)}{25-21}[/tex]

now, we can plug values

[tex]A=\frac{4576.0708-3693.88}{25-21}[/tex]

[tex]A_1=220.5477[/tex]

Average rate of change between 1 and 5 years:

we can use formula

[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]

so, we have

a=1 and b=5

[tex]f(1)=1200(1.055)^{1}=1266[/tex]

[tex]f(5)=1200(1.055)^{5}=1568.352[/tex]

[tex]A=\frac{f(5)-f(1)}{5-1}[/tex]

now, we can plug values

[tex]A_2=\frac{1568.352-1266}{5-1}[/tex]

[tex]A_2=75.588[/tex]

now, we can find ratio

[tex]\frac{A_1}{A_2}=\frac{220.5477}{75.588}[/tex]

[tex]\frac{A_1}{A_2}=3[/tex]

[tex]A_1=3A_2[/tex]

Answer:

B i took the test

Step-by-step explanation:

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