Question

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: $f(t) = 120t$
amount of savings account: $g(t) = 1,500(1.09)^t$
which function represents the amount of money henri will have after t years?
$circ (f + g)(t) = 1,500(1.09)^t + 120t, t geq 0$
$circ (f + g)(t) = 1,500 + 120t(1.09)^t, t geq 0$
$circ (f cdot g)(t) = 1,500(130.8t)^t, t geq 0$
$circ (f cdot g)(t) = 1,500(121.09t)^t, t geq 0$

Explanation:

Step1: Identify total savings logic

Total savings = shoebox savings + account savings

Step2: Sum the two functions

$(f+g)(t) = f(t) + g(t) = 120t + 1500(1.09)^t, t\geq0$

Answer:

$(f + g)(t) = 1,500(1.09)^t + 120t, t \geq 0$