Question

Victoria has $200 of her birthday gift money saved at home, and the amount is modeled by the function h(x) = 200. She reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1.05)x − 1. After combining the two functions, the new function is g(x) = 200(1.05)x − 1. Using complete sentences, explain what this new function means.

Answer 1

Given that she has $200 saved, modeled by the function

`h(x)\text{ = 200}`

The interest accrued on savings is given to be

`s(x)=(1.05)^(x-1)`

After combining the two functions, we have a new function

`g(x)=200(1.05)^(x-1)`

The above function implies that the total amount of interest received by Victoria will be evaluated as the product of the amount saved (200) and the interest rate (1.05) raised to the power of the time or duration of saving (x) minus 1.