Respuesta :
Given:
Amount in Aleka and Helene accounts represented by the following function:
Aleka: [tex]f(x) = 2500(1.025)^x[/tex]
Helene: [tex]g(x) = 1500(1.025)^x + 200x[/tex]
To find:
The function represents the difference, [tex]h(x) = f(x) -g(x)[/tex], between the value of Aleka's and Helene's total savings after x years.
Solution:
We have,
[tex]f(x) = 2500(1.025)^x[/tex]
[tex]g(x) = 1500(1.025)^x + 200x[/tex]
Now,
[tex]h(x) = f(x)-g(x)[/tex]
[tex]h(x) = 2500(1.025)^x-[1500(1.025)^x + 200x][/tex]
[tex]h(x) = 2500(1.025)^x-1500(1.025)^x - 200x[/tex]
[tex]h(x) = 1000(1.025)^x - 200x[/tex]
Therefore, the correct option is C.