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

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.