Henri puts aside $10 cash every month in a shoebox. He also makes a one-time deposit of $1,500 in a savings account at 9% annual interest, compounded yearly.Amount of shoebox savings: f(t) = 120tAmount of savings account: g(t) = 1,500(1.09)tWhich function represents the amount of money Henri will have after t years?
Answer
A
(f + g)(t) = 1,500(1.09)t + 120t, t ≥ 0
B
(f + g)(t) = 1,500 + 120t (1.09)t, t ≥ 0
C
(f ∙ g)(t) = 1,500(130.8t)t, t ≥ 0
D
(f ∙ g)(t) = 1,500(121.09t)t, t ≥ 0
Explanation
Henri’s total savings are the sum of the cash in the shoebox and the balance in the savings account. The shoebox amount after t years is 120t dollars, since he saves $10 each month for 12 months. The account balance is 1,500(1.09)^t, so the combined amount is 1,500(1.09)^t + 120t, which is choice A.
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