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)

The money is deposited into bank as principal (p) with the interest rate (r) over time (t) as year, month, etc, that money over time could be represented by:

M = p x (1 + r)^t

Here, Victoria put 200$ into bank, and that is considered the principal.

=> p = 200$

The accrue interest according to the function s(x) = (1.05)^(x−1),

=> Interest rate r is 1.05 - 1 = 0.05.

=> The function that models the total money of Victoria in that bank is:

M = 200 x (1 +0.05)^t

Hope this helps!

:)

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step-by-step explanation: