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
