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?

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?

Mercury · Answer

average rate of change from second year (x = 2) and fourth year (x = 4)

[f(4) - f(2)] / (4 - 2)

plug in x = 4 and x = 2 to find the values of f(4) and f(2) respectively, then plug them into the rate of change formula