Question

Aleka and Helene both opened savings accounts that earn 2.5% interest a year. Aleka puts $2,500 into her account. Helene put $1,500 into her account and also saves $200 cash a year. x = number of years Aleka: f(x) = 2500(1.025)x Helene: g(x) = 1500(1.025)x + 200x Which function represents the difference, h(x) = f(x) – g(x), between the value of Aleka’s and Helene’s total savings after x years?

Answer 1

Its C for those that didnt understand

Explanation:

or just to put it in short terms

Answer 2

`h(x)=1000(1.025)^x-200x`.

Explanation:

We are given function f for Aleka's amount

`f(x)=2500(1.025)^x`

And function for Helene's amount

`g(x) = 1500(1.025)^x+200x`.

Now, we need to find the difference of the functions h(x) = f(x)-g(x).

Subtracting f(x) and g(x), function, we get

`h(x) =2500(1.025)^x-(1500(1.025)^x+200x)`

Distributing minus sign over second parenthesis, we get

`h(x) =2500(1.025)^x-1500(1.025)^x-200x`

Subtracting
`2500(1.025)^x-1500(1.025)^x`, we get 1000.

Therefore,
`h(x)=1000(1.025)^x-200x`.