Suppose you are Pluto, the (immortal) god of money. Suppose the sole purpose of your existence is to accumulate as much money as possible. You don’t care about using it. You just care about having it. Suppose you currently have $1 in the Iron Bank, and the Iron Bank pays you 5% interest compounded annually. Now suppose your calculus instructor approaches you with the following proposal: If you disassociate yourself with the dirty financiers of the Iron Bank and instead invest your mighty $1 with him, he will guarantee that on the nth day after today, you will have n 10 dollars. For example tomorrow (day 1), you will have $1. The day after (day 2), you will have $1024. On day 3, you will have $59049. On day 4, you will have $1048576,...and so on. (a) Do you accept his offer? Why or why not? Here the point is to compute a limit. Set up the limit, compute it, and explain how the result explains what you should choose. (b) Would you answer change if n 10 was replaced by n 1000?
Suppose you are Pluto, the (immortal) god of money. Suppose the sole purpose of your existence is to accumulate as much money as possible. You don’t care about using it. You just care about having it. Suppose you currently have $1 in the Iron Bank, and the Iron Bank pays you 5% interest compounded annually. Now suppose your calculus instructor approaches you with the following proposal: If you disassociate yourself with the dirty financiers of the Iron Bank and instead invest your mighty $1 with him, he will guarantee that on the nth day after today, you will have n 10 dollars. For example tomorrow (day 1), you will have $1. The day after (day 2), you will have $1024. On day 3, you will have $59049. On day 4, you will have $1048576,...and so on.
(a) Do you accept his offer? Why or why not? Here the point is to compute a limit. Set up the limit, compute it, and explain how the result explains what you should choose.
(b) Would you answer change if n 10 was replaced by n 1000?
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