To determine the salary for an employee with 6 years of experience using the given data on years of experience and corresponding salaries, we can follow these steps:
1. Model Representation:
We will use a linear model to represent the relationship between years of experience ([tex]\(x\)[/tex]) and salary ([tex]\(y\)[/tex]). This model is of the form:
[tex]\[
y = mx + b
\][/tex]
where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the intercept.
2. Finding the Line of Best Fit:
Given the provided data points:
[tex]\[
(0, 52000), (1, 53150), (2, 54260), (3, 55285), (4, 56921), (5, 57126)
\][/tex]
we calculated the slope ([tex]\(m\)[/tex]) and the intercept ([tex]\(b\)[/tex]) for the best fit line. The resulting values are:
[tex]\[
m \approx 1084.8
\][/tex]
[tex]\[
b \approx 52078.33
\][/tex]
3. Using the Model to Predict Salary:
To predict the salary for 6 years of experience, substitute [tex]\(x = 6\)[/tex] into the linear model equation:
[tex]\[
y = 1084.8 \times 6 + 52078.33
\][/tex]
4. Calculating the Predicted Salary:
Plugging in the values:
[tex]\[
y \approx 1084.8 \times 6 + 52078.33 \approx 6508.8 + 52078.33 \approx 58587.13
\][/tex]
5. Rounding to the Nearest Dollar:
The predicted salary rounded to the nearest dollar is:
[tex]\[
58587
\][/tex]
Therefore, the predicted salary for an employee with 6 years of experience is [tex]\(\$58,587\)[/tex].
Among the given answer choices, the correct answer is:
[tex]\[
\boxed{\$58,587}
\][/tex]
