25 points

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. explain how victoria can combine the two functions to model the total amount of money she will have in her bank account as interest accrues after she deposits her $200. justify your reasoning.

h(x) * s(x) = 200(1.05)^(x - 1)

Step-by-step explanation:

Our interest equation is s(x) = (1.05)^(x - 1). This is actually a part of a bigger formula for calculating the amount of money accumulated including interest:

A = P(1 + r)^n, where A is the total, P is the principal amount (initial amount), r is the interest rate, and n is the time

Here, we technically already have the (1 + r)^n part; it's just (1.05)^(x - 1). The principle, though, will actually be the 200 because she starts out at $200.

Thus, to combine these, we simply multiply them together to get:

h(x) * s(x) = 200(1.05)^(x - 1)