Question: Paula took $100 from John and agreed to pay the amount after x years by using the function A(x) = 100(1.05)x. What is the average amount of money that Paula has to pay over the first 3 years?
A ) $3394 B ) $320 C ) $248 D ) $970 E ) $108
Steps to derive
1 A(x) = 100(1.05)x [Write the function.]
2 The average amount of money that Paula has to pay over the first 3 years is y‾ = 13-0∫03 100(1.05)xdx [Use 1b-a∫ab A(x) dx]
3 = 13∫03100(1.05)xdx
4 = 1003((1.05)xln(1.05))03 [Integrate.]
5 = 1003ln(1.05) [(1.05)3-1]≈ 108 [Apply the limits and simplify.]
6 The average amount of money that Paula has to pay to john over first 3 years is $108.
