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Answer :
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].
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].
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