Question

Marco makes 36,000 a year. if he receives a 5% raise, how much more money will he be getting each year?

Answer 1

He'll be making 1,800 more money per year

Answer 2

f(n)= 36,000(0.05) + 36,000 (0.05)² + 36,000 (0.05)³ +...+ 36,000 (0.05)ⁿ =

f(n)= 36,000(0.05) ( 1 +0.05 + 0.05² + ...+ 0.05ⁿ⁻¹)

Explanation:

The problem tells us that Marco makes 36,000 dollars a year, if he receives a 5% raise, we will need to multiply the current amount by 0.05 to know how much more is he getting:

`(36000)(0.05)= 1800`

However the problem doesn't end up there because on the second year he will get a 5% of the amount he will be making after the first 5% raise. So after the first year he will be getting (36,000 + 1800 = 37800) and he will get a 5% raise, so he will get a raise of

37800 (0.05)

We can write this as a function in terms of the numbers of years that have passed,

for year 1 we have that the raise will be:

f(1) = 36,000(0.05)

for the second year we will have

f(2) = 36,000 (0.05) + 36,000 (0.05)²

so for the nth year, the amount of raise will be

f(n)= 36,000(0.05) + 36,000 (0.05)² + 36,000 (0.05)³ +...+ 36,000 (0.05)ⁿ

= 36,000(0.05) ( 1 +0.05 + 0.05² + ...+ 0.05ⁿ⁻¹)