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The profit P, in millions, of Company A is given by the equation P=7.5x +17, where x is the number of years in business. The profit P, in millions, of Company B is given by the equation P=4.1x +12. Write a polynomial equation to give the "difference" in profit D after x years.

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Answer:

The polynomial equation to give the difference in profit D after x years is:

  • D = 3.4x + 5

Step-by-step explanation:

To obtain the difference in profit between the Companies A and B you can subtract the equation of company B to the equation of company A:

  • Profit Company A = 7.5x +17
  • Profit Company B = 4.1x +12
  • Difference between profits (D) = 7.5x +17 - (4.1x + 12)

And we operate:

  • D = 7.5x + 17 - 4.1x - 12
  • D = 7.5x - 4.1x + 17 - 12
  • D = 3.4x + 5

We can prove the obtained equation selecting a number of years to operate the profit equations, for example, we're gonna suppose the number of years is 3 (x = 3), we replace the formulas of profits:

  • Profit Company A = 7.5x +17
  • Profit Company A = 7.5 * (3) +17
  • Profit Company A = 22.5 +17
  • Profit Company A = 39.5 millions

  • Profit Company B = 4.1x + 12
  • Profit Company B = 4.1 * (3) + 12
  • Profit Company B = 12.3 +12
  • Profit Company B = 24.3 millions

Now, we subtract the two values:

  • Difference between profits = 39.5 millions - 24.3 millions
  • Difference between profits = 15.2 millions.

At last, using our equation with the same number of years, the calculation must give us the same value (15.2 millions):

  • D = 3.4x + 5
  • D = 3.4 (3) + 5
  • D = 10.2 + 5
  • D = 15.2

As you can see, the polynomial equation D = 3.4x + 5 is the correct to identify the difference in profit between the Companies A and B.

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