Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his investment after x years: f(x) = 300(1.02)x. What was the average rate of change of the value of Jack's investment from the third year to the fifth year?

The value of his investment at the third year is
F (3)=300×(1.02)^(3)=318.36

The value of his investment at the fifth year is
F (5)=300×(1.02)^(5)=331.22

The average rate of change of the value is
(331.22−318.36)÷2 years=6.43 per year

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InesWalston InesWalston · Answer 2 · 2018-12-02T18:54:55+01:00

Answer:

The average rate of change of Jack's investment from the third year to the fifth year is $6.43

Step-by-step explanation:

The function that defines the value of his investment after x years,

[tex]f(x)=300(1.02)^x[/tex]

Putting the value of x as 3 and 5, we can get the value of his investment after 3 years and 5 years respectively.

So,

[tex]f(3)=300(1.02)^3=318.36[/tex]

[tex]f(5)=300(1.02)^5=331.22[/tex]

Then,

[tex]\text{Average rate of change}=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

[tex]=\dfrac{331.22-318.36}{5-3}[/tex]

[tex]=\dfrac{12.86}{2}[/tex]

[tex]=\$6.43[/tex]