Tom Has Received A New Job Offer He Is Told About

Tom Has Received A New Job Offerhe Is Told That His Starting Salary W

Tom has received a new job offer! He is told that his starting salary will be $75,000.00 per year. He is also told that his salary will probably be $81,000.00 in four years. We will use this data to try to anticipate his future earnings in any given year. Assume that y = Tom's salary amount in dollars and x = the number of years worked.

Paper For Above instruction

To estimate Tom's future salary based on the given data, we will model his salary growth using a linear function. This approach assumes that Tom's salary increases at a constant rate each year, which aligns well with the data points provided. The process involves calculating the rate of change (slope), deriving the equation of the line (salary over time), and then using this model to predict future earnings.

Step 1: Calculate the rate of change (slope)

Given data points: at x = 0 years, y = $75,000; at x = 4 years, y = $81,000.

The slope (m) of the line is calculated using the formula:

m = (change in salary) / (change in years) = (81,000 - 75,000) / (4 - 0) = 6,000 / 4 = $1,500 per year.

This means that Tom's salary increases by approximately $1,500 each year.

Step 2: Write the slope-intercept form of the line

The general form of a line is y = mx + b, where m is the slope, and b is the y-intercept (initial salary).

Using the initial salary at x = 0, b = $75,000.

Therefore, the equation modeling Tom's salary is:

y = 1,500x + 75,000

This equation indicates that for each additional year worked (x), Tom's salary increases by $1,500.

Step 3: Predict Tom's salary in ten years

Substitute x = 10 into the equation:

y = 1,500(10) + 75,000 = 15,000 + 75,000 = $90,000

Thus, according to this linear model, Tom's salary in ten years will be approximately $90,000.

Conclusion

By calculating the rate of salary increase and modeling it through a linear equation, we can effectively predict Tom's future earnings. While this model provides a straightforward estimate, it assumes consistent growth and does not account for other factors such as inflation, promotions, or market changes. Nonetheless, such a model can be valuable for financial planning and setting career expectations.

References

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