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Selena2345

  • 2 years ago

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

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  1. ChristineToTheRescue
    • 2 years ago
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    So...

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

  3. Selena2345
    • 2 years ago
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    it is not an equation

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

  5. Selena2345
    • 2 years ago
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    okay

  6. ChristineToTheRescue
    • 2 years ago
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    You need an esquation to solve this...i think

  7. ChristineToTheRescue
    • 2 years ago
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    Imma work this out first. (:

  8. ChristineToTheRescue
    • 2 years ago
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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.

  9. ChristineToTheRescue
    • 2 years ago
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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.

  10. ChristineToTheRescue
    • 2 years ago
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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

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

  12. ChristineToTheRescue
    • 2 years ago
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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)

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

  14. ChristineToTheRescue
    • 2 years ago
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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

  15. Selena2345
    • 2 years ago
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    are we done with the question christine

  16. xcrypt
    • 2 years ago
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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

  17. ChristineToTheRescue
    • 2 years ago
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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

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

  19. ChristineToTheRescue
    • 2 years ago
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    there you go x3

  20. ChristineToTheRescue
    • 2 years ago
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    So...basically do the same for each day doubling it

  21. Selena2345
    • 2 years ago
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    is the question whole finish

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

  23. Selena2345
    • 2 years ago
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    is the answer finish now christine

  24. Selena2345
    • 2 years ago
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    thank you christine

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