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Selena2345

A Goblin Miner earns 1 cent the first day, 2 cents the second day 4 cents the third day, 8 cents the fourth day and so on doubling the amount each day. How much will the miner earn in 7 days ? 2 Weeks? 1 Month ( Make An Estimate Before Solving) Show/ Explain All Work

  • one year ago
  • one year ago

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  1. ChristineToTheRescue
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    So...

    • one year ago
  2. ChristineToTheRescue
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    Um, I'm not so sure how to put this in an equation...

    • one year ago
  3. Selena2345
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    it is not an equation

    • one year ago
  4. ChristineToTheRescue
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    But, you can estimate obviously that it's about 70

    • one year ago
  5. Selena2345
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    okay

    • one year ago
  6. ChristineToTheRescue
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    You need an esquation to solve this...i think

    • one year ago
  7. ChristineToTheRescue
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    Imma work this out first. (:

    • one year ago
  8. ChristineToTheRescue
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    We see that the series whose sum gives the total number of cents follows a regular pattern: each new term added to it is a power of two. This is an example of a geometric series.

    • one year ago
  9. ChristineToTheRescue
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    In our case, we are told that the number of cents given each day is double the number given the day before, which suggests that the ratio of this series is 2.

    • one year ago
  10. ChristineToTheRescue
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    no. pennies given on second day 2 ------------------------------- = 2 no. pennies given on first day 1 no. pennies given on third day 4 ------------------------------- = 2 no. pennies given on second day 2 no. pennies given on fourth day 8 ------------------------------- = 2 no. pennies given on third day 4

    • one year ago
  11. ChristineToTheRescue
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    obviously, the ratio of the geometric series that gives the total number of cents on a particular day is 2.

    • one year ago
  12. ChristineToTheRescue
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    we can use the fact that the sum of a geometric series (called S) with n terms whose ratio is r is this S = (first term)(1-r^n)/(1-r)

    • one year ago
  13. ChristineToTheRescue
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    I think... ><'' not very expertise on this but had hw on this like 2 wks ago.

    • one year ago
  14. ChristineToTheRescue
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    This means that for our series with a first term of 1 and a ratio of 2, we find the sum after n days = 1(1 - 2^n) / (1 - 2) = - (1 - 2^n) = 2^n - 1

    • one year ago
  15. Selena2345
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    are we done with the question christine

    • one year ago
  16. xcrypt
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    The equation would be: 2^x-1, where x represents the day. substitute 7 for x and you have your answer

    • one year ago
  17. ChristineToTheRescue
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    1 2^1-1 = 2-1 = 1 2 2^2-1 = 4-1 = 3 3 2^3-1 = 8-1 = 7 4 2^4-1 = 16-1 = 15

    • one year ago
  18. xcrypt
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    I am sorry, 2^(x-1)

    • one year ago
  19. ChristineToTheRescue
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    there you go x3

    • one year ago
  20. ChristineToTheRescue
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    So...basically do the same for each day doubling it

    • one year ago
  21. Selena2345
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    is the question whole finish

    • one year ago
  22. ChristineToTheRescue
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    5 2^5-1 = 18-1 = 17 and so forth

    • one year ago
  23. Selena2345
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    is the answer finish now christine

    • one year ago
  24. Selena2345
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    thank you christine

    • one year ago
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