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Question: 

I agree to hire you for 30 days. You can decide between two methods of payment: either

  1. $1000 a day, or
  2. one penny on the first day, two pennies on the second day and continue to double your daily pay each day up to day 30.

Use quick estimation to make your decision, and justify it.

Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014. Reprinted by permission of Pearson Education Inc., New York.
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Quick Answer: 

option 1: \$30, 000 total
option 2: \$10, 737, 418 on the last day alone

Giancoli 7th Edition, Chapter 1, Problem 33

(1:40)

Chapter 1, Problem 33 is solved.

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Transcript for this Giancoli solution

This is Giancoli Answers with Mr. Dychko. For option 1 where you get $1000 dollars a day times 30 days will give you a total of $30,000 dollars after 30 days. For option 2, it says use quick calculation so I'm just gonna calculate what would the pay be on just the single last day with the scheme where you start with one penny the first day and then double it for thirty days and on last day alone, you would make 10,737,418 on the last day alone; nevermind, half of that in the day before and then half that again in the day prior to that. You know, you could figure out the sum of the geometric series if you wanted to but just based on this pay on last day alone, it's clear that option 2 is way better choice and if this number is a surprise for you then you need to know about compound interest; investing early is always good.