Question

A professional athlete signs a five-year contract in which the earnings can be modeled by c=300,000+450,000t, where t represents the year

Answer 1

The annual pay is c(t) = 300,000 + 450,000·t. (Assuming t = 1 for year 1, …, t = 5 for year 5.)

- Year 1 (t=1): c = 300,000 + 450,000(1) = 750,000
- Year 2 (t=2): c = 1,200,000
- Year 3 (t=3): c = 1,650,000
- Year 4 (t=4): c = 2,100,000
- Year 5 (t=5): c = 2,550,000

Annual increase: 450,000 each year.

Total paid over the five years = 750,000 + 1,200,000 + 1,650,000 + 2,100,000 + 2,550,000 = 8,250,000.

(If instead t were counted from 0 to 4, then year 1 would be t=0 and c=300,000; clarify your convention if needed.)