Question

Jason Witten's Salary Negotiation Let's say that tight end Jason Witten (a football player) was given two options when negotiating his contract for the 2017 football season (which was his final season, ). Option 1 was that he would be paid an additional $0.01 (yes one red cent) if he makes only one catch for the season, $0.02 if he makes a total of two catches, $0.04 for a total of three catches and so on, doubling the amount with each catch. Option 2 was that he would be paid a flat $2,000,000 increase from the previous year. Basing this decision on the 2012 season (where he had a career high of 110 total receptions/catches), which option would increase his salary more? (In other words, is it better for him to be paid per catch, starting with 1 cent and doubling with each catch up to 110 or is it better to have a flat $2 million increase?)

Answer 1

To increase Jason Witten's salary more, he should choose Option 2, which offers a flat $2,000,000 increase. Option 1, which pays progressively more for each catch, would result in significantly lower earnings.

Step-by-step explanation:

To determine which option would increase Jason Witten's salary more, we need to calculate the total amount he would earn under each option. Option 1 pays Jason progressively more for each catch, starting with $0.01 and doubling with each catch. Option 2 offers a flat $2,000,000 increase. Let's calculate the earnings under both options:

Option 1:

Jason's career high in catches is 110, so we will calculate the earnings up to that point. The formula for summing a geometric series is S = a * (r^n - 1) / (r - 1), where a is the first term, r is the common ratio, and n is the number of terms. In this case, a = 0.01, r = 2, and n = 110. Plugging these values into the formula, we get: S = 0.01 * (2^110 - 1) / (2 - 1) = 0.01 * (2^110 - 1).

Option 2:

Option 2 offers a flat $2,000,000 increase, so Jason's earnings under this option would be $2,000,000.

Comparing the earnings under both options, we can see that the amount earned under Option 2 is significantly higher than under Option 1. Therefore, Option 2 would increase Jason Witten's salary more.

Answer 2

Option 1: It is better for him to be paid per catch, starting with 1 cent and doubling with each catch up to 110

Step-by-step explanation:

If Jason were to be paid per catch given that he makes a total of 110 catches for the 2017 season in his new contract, he would make a total of :

0.01 × 2^109 = $6.4903711e+30(calculator result, means 6 then 30 digits after)

Therefore it is better for Jason to be paid per catch and not a flat fee of $2000000