Answer :
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]
[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]