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

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

mathstudent55 · Answer

I assume the x is an exponent.
First, find f(4). Then find f(2). Then subtract their values and divide by 2.

anonymous · Answer

Yes

wolf1728 · Answer

That formula should actually be:
Total = Principal * (1 + rate) ^ years
and I guess we assume the principal is $500

as mathstudent55 said we must find f(4) which is
500*(1.05)^4 = 607.75
Then find f(2) which is
500*(1.05)^2 = 551.25

607.75 -551.25 = 56.50 for 2 years
or 28.25 per year which looks like it's the second answer