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The Greek God Zeus ordered his blacksmith Hephaestus to create a perpetual water-making machine to fill Zeus' mighty chalice. The volume of Zeus' chalice was reported to hold about one hundred and fifty sextillion gallons (that is a fifteen followed by twenty-two zeros). If Hephaetus' machine pours out 2 gallon in the first minute and then doubles its output each minute, find in which minute would this hypothetical machine pour out a single quantity of water that would be enough to fill Zeus' chalice with water?
1 hr, 2 min

  • algebra -

    1st. min--2gal. = 2^1.
    2nd. " ---4gal. = 2^2.
    3rd. " ---8gal. = 2^3.
    4th. " ---16gal.= 2^4.

    nth. min.--15*10^22gal. = 2^x.

    2^x = 15*10^22
    x*Log2 = Log(15*10^22
    x*Log2 = Log15+Log10^22
    x*Log2 = Log15 + 22*Log10
    x*Log2 = 1.17609 + 22
    x*Log2 = 23.17609
    Divide both sides by Log2:
    X = 76.98931.

    77th.min.---15*10^22gal = 2^77.

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