Chapter 4.1, Problem 72E

Comparing rates of change. Jim is offered a job that will pay him $50 in the first day, $100 on the second day, $150 on the third day, and so on; thus, the rate of change of his pay t days after starting the job is given by $J\text{'}\left(t\right)=50$

Larry is offered the same job, but the rate of change of this his pay is given by $L\text{'}\left(t\right)=e^{0.1t},$

Both $J\text{'}\left(t\right)$ and $L\text{'}\left(t\right)$ are measured in dollars per day.

a. Determine the total pay model for Jim and for Larry.

b. After 30 day, what is Jim’s total pay and Larry’s total pay?

c. On what day does Larry’s dally pay first exceed Jim’s dally pay?

d. In general, how does exponential growth compare to linear growth? Explain.