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A company determines an employee's starting salary according to the number of years of experience, as detailed in the table below:

\begin{tabular}{|l|c|}
\hline
Years of Experience & Salary \\
\hline
0 & \[tex]$40,000 \\
\hline
1 & \$[/tex]42,150 \\
\hline
2 & \[tex]$44,260 \\
\hline
3 & \$[/tex]46,785 \\
\hline
4 & \[tex]$48,820 \\
\hline
5 & \$[/tex]51,126 \\
\hline
\end{tabular}

Use the equation for the line of best fit to predict the salary for an employee with 7 years of experience. (Round your answer to the nearest dollar.)

A. \[tex]$52,900
B. \$[/tex]53,340
C. \[tex]$53,914
D. \$[/tex]55,573



Answer :

GinnyAnswer
Let's follow the steps to determine the predicted salary for an employee with 7 years of experience.

1. Identify the variables:
- Years of experience ([tex]\( x \)[/tex]): [0, 1, 2, 3, 4, 5]
- Salary ([tex]\( y \)[/tex]) in dollars: [40000, 42150, 44260, 46785, 48820, 51126]

2. Determine the equation of the line of best fit:
The line of best fit can be described by the equation [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

3. Calculate the slope ([tex]\( m \)[/tex]) and the y-intercept ([tex]\( b \)[/tex]) of the line:
- Slope [tex]\( m = 2233.29 \)[/tex]
- Y-intercept [tex]\( b = 39940.29 \)[/tex]

4. Formulate the linear equation for the line of best fit:
- The equation derived from the data is [tex]\( y = 2233.29x + 39940.29 \)[/tex]

5. Predict the salary for 7 years of experience:
- Let [tex]\( x = 7 \)[/tex]
- Substitute [tex]\( x = 7 \)[/tex] into the equation [tex]\( y = 2233.29x + 39940.29 \)[/tex]

[tex]\[ y = 2233.29 \times 7 + 39940.29 \][/tex]

6. Calculate the predicted salary:

[tex]\[ y = 2233.29 \times 7 + 39940.29 \][/tex]
[tex]\[ y = 15632.99 + 39940.29 \][/tex]
[tex]\[ y = 55573 \][/tex]

7. Round the predicted salary to the nearest dollar:
- The predicted salary for an employee with 7 years of experience is [tex]\( \$55,573 \)[/tex].

So, the correct answer is:
- [tex]\(\$ 55,573\)[/tex]

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