Jack and Susie want to save to buy a trampoline for their children. They each open a savings account with an interest rate of [tex]$1.5\%$[/tex] per year. Jack opens his account with [tex]$\$[/tex]1,000[tex]$, and Susie opens her account with $[/tex]\[tex]$800$[/tex].

The following functions represent the value of the savings accounts in [tex]$x$[/tex] years:

- Jack's savings account: [tex]f(x) = 1000(1.015)^x[/tex]
- Susie's savings account: [tex]g(x) = 800(1.015)^x[/tex]

Which function represents the total amount Jack and Susie will save in [tex]$x$[/tex] years?

A. [tex]200(1.015)^x[/tex]

B. [tex]1800(1.015)^{2x}[/tex]

C. [tex]1800(1.030)^x[/tex]

Jack's savings account is given by
[tex]$$
f(x)=1000(1.015)^x,
$$[/tex]
and Susie's savings account is given by
[tex]$$
g(x)=800(1.015)^x.
$$[/tex]

To find the total amount saved in [tex]$ x $[/tex] years, add the two functions:
[tex]$$
\text{Total savings} = f(x)+g(x)=1000(1.015)^x+800(1.015)^x.
$$[/tex]

Since both terms have the common factor [tex]$ (1.015)^x $[/tex], factor it out:
[tex]$$
\text{Total savings} = (1000+800)(1.015)^x.
$$[/tex]

Simplify the sum inside the parentheses:
[tex]$$
1000 + 800 = 1800.
$$[/tex]

Thus, the total savings function becomes:
[tex]$$
\text{Total savings} = 1800(1.015)^x.
$$[/tex]

Therefore, the function that represents the total amount Jack and Susie will save in [tex]$ x $[/tex] years is
[tex]$$
1800(1.015)^x.
$$[/tex]