Jack and Susie want to save to buy a trampoline for their children. They each open a savings account that earns [tex]$1.5\%$[/tex] a year. Jack opens his account with [tex]$1000[/tex], and Susie opens her account with [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)^x[/tex]
C. [tex]1800(1.015)^{2x}[/tex]
D. [tex]1800(1.030)^x[/tex]

To determine which function represents the total amount Jack and Susie will save in [tex]$ x $[/tex] years, let's go through the steps:

1. Identify Each Individual's Savings:
- Jack's Savings: Jack starts with [tex]$1,000 in his savings account, which earns 1.5% interest per year. This can be represented by the function:
\[
f(x) = 1000 \times (1.015)^x
\]
- Susie's Savings: Susie starts with $[/tex]800 in her savings account, which also earns 1.5% interest per year. This can be represented by the function:
[tex]\[
g(x) = 800 \times (1.015)^x
\][/tex]

2. Combine Their Savings:
- To find the total savings of both Jack and Susie, we simply add their individual savings functions:
[tex]\[
\text{Total savings} = f(x) + g(x) = 1000 \times (1.015)^x + 800 \times (1.015)^x
\][/tex]

3. Factor the Combined Function:
- Factor out the common term [tex]$ (1.015)^x $[/tex]:
[tex]\[
\text{Total savings} = (1000 + 800) \times (1.015)^x
\][/tex]
- Simplify the expression inside the parentheses:
[tex]\[
= 1800 \times (1.015)^x
\][/tex]

4. Conclusion:
- The function that represents the total amount Jack and Susie will save in [tex]$ x $[/tex] years is [tex]$ 1800 \times (1.015)^x $[/tex].

Therefore, the correct answer is [tex]$ 1800(1.015)^x $[/tex].