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

@nikato

Answer 2

i think the first thing to do is calculate for the second year and for the fourth year

Answer 3

I think it is important to get the formula correct also:
instead of this
f(x) = 500(1.05) Use this
total = principal * (1 + rate) ^time
(notice we need exponentiation here.)

Answer 4

Well, since everyone has left, I might as well post the answer.

total = principal * (1 + rate) ^time
For year zero this calculates to
500.00 = 500.00 * (1.05)^0
525.00 = 500.00 * (1.05)^1
551.25 = 500.00 * (1.05)^2
578.81 = 500.00 * (1.05)^3
607.75 = 500.00 * (1.05)^4
Year 4 - Year 2 amount =
607.75 -551.25 which equals
56.50 per TWO years or
(56.50 / 2) = 28.25 per year.

Answer 5

Thank you, wolf1728!