Question

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?

Answer 1

The equation is f(x) = 300 * (1.02)^x

1) Evaluate the equation for x = 3 years and x = 5 years

x = 3 => f(3) = 300 * (1.02)^3 = $318.3624

x= 5 => f(5) = 300 * (1.02)^5 = $331.2242

2) The average rate of change is [change in f(x) ] / [change in x]

change in f(x) = f(5) - f(3) = $12.8678

change in x = 5year - 3 year = 2 year

Average rate of change = $12.8678 / 2 year = $6.43 / year <---- answer

Answer 2

Jack's investment on the third year
f(3) = 300(1.02)³ = 318.36 (rounded to 2 decimal place)

Jack's investment on the fifth year
f(5) = 300(1.02)⁵ = 331.22 (rounded to 2 decimal place)

The average rate of change from year 3 to year 5 = (331.22 - 318.36) ÷ (5 - 3)
The average rate of change = 12.86 ÷ 2 = 6.43