Question

n 1895, the first Putting Green Championship was held. The winner’s prize money was $200. In 2016, the winner’s check was $1,480,000. a. What was the percentage increase per year in the winner’s check over this period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. If the winner’s prize increases at the same rate, what will it be in 2043?

Answer 1

Answer:

• 7.64% per year
• $10,805,480 . . . . rounded to 7 significant figures

Step-by-step explanation:

Using 2016 as a reference (t=0), the exponential equation for winnings can be written as ...

  w(t) = 1480000×(1480000/200)^(t/121)

where 1480000 is the winnings in the reference year, and the ratio 1480000/200 is the ratio of winnings increase over the 121 years from 1895 to 2016.

This can be approximated by ...

  w(t) ≈ 1,480,000×1.07640850764^t

In this form, we can see that the annual percentage increase is ...

  1.0764 -1 = 7.64%

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Then the winner's check in 2043, 27 years after 2016, is predicted to be ...

  w(27) = $1,480,000×(1.0764...)^27 ≈ $10,805,478.41 ≈ $10,805,000