linear model

Question

Given that percent can be expressed in decimal form (example: 25% of a value y can be written as 0.25y) answer the following:

Tom uses the linear model of y = 35,000 + 0.45x to anticipate his salary from completing x amount of dollars' worth of jobs.

1. What is Tom's base salary? What percent commission does he earn? Would you be able to use the same equation for Tom the next year? Why or why not?

Answer 1

Tom uses the linear model of y = 35,000 + 0.45x to anticipate his salary from completing x amount of dollars' worth of jobs.  What is Tom's base salary? What percent commission does he earn? Would you be able to use the same equation for Tom the next year? Why or why not?

x= the amount of dollars worth of jobs.  So if x = 0, then y = $35,000 + 0.45(0) = $35,000.  So that's Tom's base salary (the smallest amount he earns, even if no jobs are performed).

 

Tom's commission is his percentage of $ from each job.  If x = the amount of dollars worth of jobs, then Tom gets 0.45 of that, or 45% commission.

 

We could use the same formula for Tom's salary next year unless his base salary is raised or his commission changes.  Any price increase charged to customers for work next year would be reflected in greater values of x, but the formula would stay the same unless either the base salary or commission change.