You have just landed your first summer job and your boss has told you that you can choose from one of 3 pay structures for the first week (7 days) that you work there. And after the first week, your pay will be frozen at the final rate for the remainder of the summer.

Question

#1pay structure-1,3,5,7,9,11,13
#2pay structure-1,4,9,16,25,36,49
#3pay structure-1,2,4,8,16,32,64
1. Which option would you choose? Defend your decision mathematically.
2. Describe each option as linear, quadratic or exponential. Prove your description using finite differences.

Answer 1

3 obviously, 64 from now on is better than 49 or 13

1. linear, slope = 2

2. quadratic, 1^2 2^2 3^2 ..... 7^2

3. exponential 2^n

Answer 2

Thanks so much!