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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.

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User Troy Hunt
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To model the total amount of money Victoria will have in her bank account as interest accrues after she deposits her $200, we can combine the two functions h(x) and s(x).The function h(x) represents the initial amount of money Victoria has saved at home, which is $200. The function s(x) represents the interest rate of the savings account, where x represents the number of years the money is left in the account. So, if Victoria deposits her $200 into the savings account and leaves it there for x years, the amount of money in her account will be:h(x) + h(x) * s(x)Substituting the values for h(x) and s(x), we get:$200 + $200 * (1.05)x-1This is the total amount of money Victoria will have in her bank account as interest accrues after she deposits her $200. The function combines the initial amount of money saved with the interest rate of the savings account over time, as represented by the function s(x). The interest rate is compounded annually, which is why the function s(x) uses an exponent of x-1.Therefore, Victoria can use this function to calculate the amount of money in her bank account after depositing her $200 and leaving it in the savings account for a certain number of years.

User Milan Jaros
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