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]
