We are told that the initial salary of an employee is $ 30 000 and the salary increases at a fixed rate of 5 % at the end of each year. Therefore, we can represent the salary at the n^(th) year s( n) with an exponential function. To do so, let's remember how we can model an exponential growth with a function.
A( t) = a(1+ r)^t
In this form, A( t) represents the amount after t time periods, a represents the initial amount, r is the rate of growth, and t is the number of time periods. Let's match those variables to ours.
Substitution
A( t)
s( n)
a
$ 30 000
r
5 %= 0.05
t
n-1
Note that we express the number of time periods as n-1 because the person receives a 5 % raise at the end of each year. Since we want to calculate the total amount at the beginning of the year, it would be the same with the previous year. Therefore, we need to substitute n-1 to calculate the salary at the n^(th) year. Let's now substitute all the variables!
