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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. satellite73
    • 2 years ago
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    7 days is easy 1+2+4+8+16+32+64

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

  3. satellite73
    • 2 years ago
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    you have \(1, 2, 2^2, 2^3, 2^4, ...\)

  4. Selena2345
    • 2 years ago
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    Are your answering the question right

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

  6. Selena2345
    • 2 years ago
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    Are your answering the question right

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

  8. CliffSedge
    • 2 years ago
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    I want that job if I get to work the whole month!

  9. satellite73
    • 2 years ago
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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

  10. Selena2345
    • 2 years ago
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    can u help cliffSedge

  11. Selena2345
    • 2 years ago
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    yes cliffsedge thank you

  12. CliffSedge
    • 2 years ago
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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.)

  13. CliffSedge
    • 2 years ago
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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.

  14. CliffSedge
    • 2 years ago
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    But satellite's formula is a lot quicker. ;-)

  15. Selena2345
    • 2 years ago
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    thank you agent47

  16. Agent47
    • 2 years ago
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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

  17. Agent47
    • 2 years ago
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    I think, satellite's made a mistake.. but that's IMPOSSIBRU!

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

  19. Agent47
    • 2 years ago
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    woah waitttt

  20. Agent47
    • 2 years ago
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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

  21. Selena2345
    • 2 years ago
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    is the answer to the question finish

  22. Agent47
    • 2 years ago
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    Not yet... the formula is: |dw:1347412596200:dw|

  23. satellite73
    • 2 years ago
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    actually i gave the total earned on day \(n\) not the amount earned on day \(n\)

  24. Agent47
    • 2 years ago
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    ya you're right, i just realized that

  25. Selena2345
    • 2 years ago
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    is the answer to the question finish

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

  27. Agent47
    • 2 years ago
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    ok i see, then that's the final answer... satellite why are u so smart?

  28. Selena2345
    • 2 years ago
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    who's correct satellite or agent47

  29. Agent47
    • 2 years ago
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    satellite, obv, who's a level 100 here?

  30. Agent47
    • 2 years ago
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    but i did realize my mistake, before satellite pointed it out :P

  31. Selena2345
    • 2 years ago
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    who's correct satellite or agent47

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