Answer:
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)
Step-by-step 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:
[tex](36000)(0.05)= 1800[/tex]
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)
