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For an analysis of the salaries of your​ company, you plot the salaries of all employees against the number of years they have worked for the company. You find that plotting the​ base-10 logarithm of salary makes the plot much straighter. A​ part-time shipping​ clerk, who has worked at the company for one year earns ​$12 comma 000. A manager earns ​$120 comma 000 after 20 years with the firm. The​ CEO, who founded the company 40 years​ ago, receives ​$1 comma 500 comma 000. What are the values you will​ plot? Will the plot of these three points be straight​ enough?

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Edufirst

Answer:

1. That values that you must plot are:

  • (1, 4.08))
  • (20, 5.08)
  • (40, 6.18)

2. Yes, the plot of those three points is straight enough.

Explanation:

A. What are the values you will​ plot?

The x-ccordinate of your plot is still the number of years the exmployees have worked for the company.

The y-coordinate of your plot is the the​ base-10 logarithm of  the salary.

Therefore:

1) A​ part-time shipping​ clerk: 1 year, $12,000

           ⇒     [tex](1,log_{10}12,000)=(1,4.08)[/tex]

2) A manager: 20 years, $120,000

  ⇒     [tex](20,log_{10}120,000)=(20,5.08)[/tex]

3) The​ CEO: 40 years​ ago, $1,500,000

  ⇒     [tex](40,log_{10}1,500,000)=(40,6.18)[/tex]

Summarizing, the points to plot are:

  • (1, 4.08)
  • (20, 5.08)
  • (40, 6.18)

B. Will the plot of these three points be straight​ enough?

To find whether the plot is straight enoguh, you may either plot them, make a regression, or, since they are only three points, you can whether the change of rate of the points is constant.

  • Change of rate of the first two points, r:

       r = rise/run = Δy / Δx = (5.08 - 4.08) / (20 - 1) =1.00/19 ≈ 0.05

  • Change of rate of the second and the third points, r:

       r = rise/run = Δy / Δx = (6.18 - 5.08) / (20 - 1) = 0.05

Since both rate of changes are equal (or reasonably equal) the plot is  straight enough.

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