Let's solve the problem with the information given.
Wyatt's initial salary and the yearly raise are as follows:
- Initial salary: \[tex]$35,000
- Yearly raise: \$[/tex]2,000
He will receive this yearly raise for every year he works at the company.
1. Determine the Variables:
- The independent variable, [tex]\( x \)[/tex], represents the number of years working at the company.
- The dependent variable is the salary, denoted as [tex]\( Z \)[/tex], because the salary depends on the number of years worked.
2. Form the Function Relating the Variables:
- The formula to calculate the salary after [tex]\( x \)[/tex] years is:
[tex]\[
Z(x) = \text{initial salary} + (\text{yearly raise} \times x)
\][/tex]
Plugging in the values, we get:
[tex]\[
Z(x) = 35000 + (2000 \times x)
\][/tex]
3. Calculate the Salary After 8 Years:
- To find out the salary after 8 years [tex]\( ( x = 8 ) \)[/tex]:
[tex]\[
Z(8) = 35000 + (2000 \times 8)
\][/tex]
[tex]\[
Z(8) = 35000 + 16000
\][/tex]
[tex]\[
Z(8) = 51000
\][/tex]
Putting it all together, we can answer the questions step-by-step:
- The independent variable, [tex]\( x \)[/tex], represents the number of years.
- The dependent variable is the salary, because the salary depends on the number of years.
A function relating these variables is [tex]\( Z(x) = 35000 + 2000x \)[/tex].
So [tex]\( Z(8) = 51000 \)[/tex], meaning 8 years leading to a salary of \$51,000.
This detailed solution outlines the relationship between Wyatt's salary and the number of years he works at the company, demonstrating how to calculate the changes over time.
