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.
Option 1 - You are paid $1 on the first day, and then $2 more each day that follows (i.e., $3, $5, $7, ... for the rest of the 7 days.
Option 2 - You are paid $1 the first day, then $4 the next day, then $9 the day after that, then $16, then $25, and so on for the rest of the 7 days.
Option 3 - You are paid $1 the first day, then two times that amount on the second day ($2), then two times that amount the next day ($4), then $8, $16, and so on for the rest of the week.
Which option would you choose? Defend your decision mathematically.
How much money would you have at the end of the 7 days if you choose each option?
Describe each option as linear, quadratic or exponential. Prove your description using finite differences.
State two reasons why "money isn't everything" when it comes to a job.
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