Question

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

b. What does the number $75,000 represent in the context of this problem?

Answer 1

In the context of the problem, $75,000 represents Carmela's initial salary.

Explanation:

Her salary is modeled by the following function:

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

So

At any time we have a function modeled in this following recursive format:

`C_{n+1) = F(C_(n))`

We have that
`C_(0)` is the initial value of C.

For this problem, we have that C is Carmela's salary. So
`C_(0) = 75,000` is Carmela's initial salary. This means that in the context of the problem, $75,000 represents Carmela's initial salary.