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Selena2345 Group Title

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. satellite73 Group Title
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    7 days is easy 1+2+4+8+16+32+64

    • one year ago
  2. satellite73 Group Title
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    you might notice that this is 127, one less than 2 times 64

    • one year ago
  3. satellite73 Group Title
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    you have \(1, 2, 2^2, 2^3, 2^4, ...\)

    • one year ago
  4. Selena2345 Group Title
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    Are your answering the question right

    • one year ago
  5. satellite73 Group Title
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    in 7 days you will have earned \(2^7-1=\$1.27\)

    • one year ago
  6. Selena2345 Group Title
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    Are your answering the question right

    • one year ago
  7. satellite73 Group Title
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    in two weeks you will have \(2^{4}-1\) pennies, a calculator gives \(\$163.83\)

    • one year ago
  8. CliffSedge Group Title
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    I want that job if I get to work the whole month!

    • one year ago
  9. satellite73 Group Title
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    me too in one month of 31 days you will have made \(2^{31}-1\) pennies, more money than i will earn in several life times

    • one year ago
  10. Selena2345 Group Title
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    can u help cliffSedge

    • one year ago
  11. Selena2345 Group Title
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    yes cliffsedge thank you

    • one year ago
  12. CliffSedge Group Title
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    If you have a calculator, you can try entering '1' then hitting x2 a bunch of times (counting how many times you do so.)

    • one year ago
  13. CliffSedge Group Title
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    Of course, that will only get you the per day earnings. You'll have to add up all the previous days' to get the total.

    • one year ago
  14. CliffSedge Group Title
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    But satellite's formula is a lot quicker. ;-)

    • one year ago
  15. Selena2345 Group Title
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    thank you agent47

    • one year ago
  16. Agent47 Group Title
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    Let x be the amt u earn per day... Then, in 1 day: 1cent = 2^0 cents 2 days: 2 cents = 2^1 cents 3 days: 4 cents = 2^2 cents 4 days: 8 cents = 2^3 cents... So, in n days, you get 2^(n-1) cents

    • one year ago
  17. Agent47 Group Title
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    I think, satellite's made a mistake.. but that's IMPOSSIBRU!

    • one year ago
  18. Agent47 Group Title
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    Thus, in 7 days: 2^(7-1)=2^6=64 cents

    • one year ago
  19. Agent47 Group Title
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    woah waitttt

    • one year ago
  20. Agent47 Group Title
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    That is the amount he earned on the 1st, 2nd, 3rd, 4th, etc days, and on the 7th day he earns 64 cents

    • one year ago
  21. Selena2345 Group Title
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    is the answer to the question finish

    • one year ago
  22. Agent47 Group Title
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    Not yet... the formula is: |dw:1347412596200:dw|

    • one year ago
  23. satellite73 Group Title
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    actually i gave the total earned on day \(n\) not the amount earned on day \(n\)

    • one year ago
  24. Agent47 Group Title
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    ya you're right, i just realized that

    • one year ago
  25. Selena2345 Group Title
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    is the answer to the question finish

    • one year ago
  26. satellite73 Group Title
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    on day \(n\) you earn \(2^{n-1}\) pennies, for a total of \(2^n-1\) pennies

    • one year ago
  27. Agent47 Group Title
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    ok i see, then that's the final answer... satellite why are u so smart?

    • one year ago
  28. Selena2345 Group Title
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    who's correct satellite or agent47

    • one year ago
  29. Agent47 Group Title
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    satellite, obv, who's a level 100 here?

    • one year ago
  30. Agent47 Group Title
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    but i did realize my mistake, before satellite pointed it out :P

    • one year ago
  31. Selena2345 Group Title
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    who's correct satellite or agent47

    • one year ago
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