Question

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

c. Find an explicit formula for a sequence that represents Carmela’s salary.

Answer 1

Answer:
`C_n=75000(1.05)^n,\text{ for}n\geq0`

Explanation:

Given : Carmela’s annual salary in year n can be modeled by the recursive sequence
`C_(n+1) = 1.05 C_n`, where
`C_0` = $75,000.

It is a geometric sequence with common ratio r= 1.05

Explicit formula for geometric sequence:-

`a_n=a_0r^n,\text{ for}n\geq0`

An explicit formula for a sequence that represents Carmela’s salary will be:

`C_n=C_0(1.05)^n,\text{ for}n\geq0`

`C_n=75000(1.05)^n,\text{ for}n\geq0`