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? h(x) = –1000(1.025)x + 200x h(x) = 1000(1.025)x + 200x h(x) = 1000(1.025)x – 200x h(x) = 4000(1.025)x + 200x

Answer 1

c

Explanation:

Answer 2

Given:

Amount in Aleka and Helene accounts represented by the following function:

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

Helene:
`g(x) = 1500(1.025)^x + 200x`

To find:

The function represents the difference,
`h(x) = f(x) -g(x)`, between the value of Aleka's and Helene's total savings after x years.

Solution:

We have,

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

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

Now,

`h(x) = f(x)-g(x)`

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

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

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

Therefore, the correct option is C.