Question

sophia invested some money in a bank at a fixed rate of interest compounded annually. the equation below shows the value of her investment after x years: f(x) = 500(1.05)x what was the average rate of change of the value of sophia's investment from the second year to the fourth year? 14.13 dollars per year 28.25 dollars per year 50.00 dollars per year 56.50 dollars per year

Answer 1

$f(2)=500(1.05)^{2}= 551.25$
$f(4)=500(1.05)^{4}= 607.75$
The change in value over 2 years = $607.75 - $551.25 = $56.50.
Therefore the average rate of change is $56.50 / 2 = $28.25 per year.
The second choice is correct.

Answer 2

The average rate of change of the value of Sophia's investment from the second year to the fourth year will be $28.25 per year. Then the correct option is B.

What is the average rate of change?

The change in function to the change in variable.

Sophia invested some money in a bank at a fixed rate of interest compounded annually.

The equation below shows the value of her investment after x years:

f(x) = 500(1.05)ˣ

Then the average rate of change of the value of Sophia's investment from the second year to the fourth year will be

Average rate of change = [f(4) – f(2)] / [4 – 2]

Average rate of change = [{500(1.05)⁴} – {500(1.05)²}] / 2

Average rate of change = 56.50 / 2

Average rate of change = 28.25

Then the correct option is B.

More about the average rate of change link is given below.

https://brainly.com/question/23715190

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