Question

55. Carmela’s annual salary in year n can be modeled by the recursive sequence Cn+1 = 1.05 Cn, where C0 = $75,000.

a. What does the number 1.05 represent in the context of this problem?

Answer 1

It represents that Carmela's salary increases 5 percent each year.

Explanation:

Her salary is modeled by the following function:

`C_(n+1) = 1.05C_(n)`

So

`(C_(n+1))/(C_(n))= 1.05`

This means that for each year, Carmela's next year salary is going to 1.05 of this year.

So, in the context of this problem, the number 1.05 represents that Carmela's salary increases 1.05-1 = 0.05 = 5 percent each year.