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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]\[tex]$1000[/tex], and Susie opens her account with [tex]\$[/tex]800[/tex].

Let [tex]x[/tex] be the number of years.

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?

[tex]
\begin{array}{l}
A. 200(1.015)^x \\
B. 1800(1.015)^x \\
C. 1800(1.015)^{2x} \\
D. 1800(1.030)^x
\end{array}
[/tex]



Answer :

GinnyAnswer
To determine the function that represents the total amount Jack and Susie will save in [tex]\( x \)[/tex] years, we need to add their individual savings functions together.

Jack's savings account is given by:
[tex]\[ f(x) = 1000(1.015)^x \][/tex]

Susie's savings account is given by:
[tex]\[ g(x) = 800(1.015)^x \][/tex]

To find the total amount they will save together, we add these two functions:
[tex]\[ f(x) + g(x) = 1000(1.015)^x + 800(1.015)^x \][/tex]

We can factor out the common term [tex]\( (1.015)^x \)[/tex] from both expressions:
[tex]\[ f(x) + g(x) = (1000 + 800)(1.015)^x \][/tex]

Simplifying inside the parentheses:
[tex]\[ f(x) + g(x) = 1800(1.015)^x \][/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]

Among the given options, the correct one is:
[tex]\[ 1800(1.015)^x \][/tex]

So the correct answer is:
[tex]\[ \boxed{1800(1.015)^x} \][/tex]

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