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March 25, 2017

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your aunt gives you a check on your birthday each year. on your first birthday , she gives you a check for one cent. the next year she gives you 3 cents , then 9. each year she triples the amount of the previous year 's check. how old will you be when she gives you a check worth more than 1000$ ? how much money will you receive on your 18th birthday?

  • Math - ,

    1c. = 3^0,
    3c = 3^1,
    9c. = 3^2,
    27c = #^3.
    So we have base 3 numerals.
    A = 3^(n-1). A = Amount in cents @ nth year.

    a. 3^(n-1) = 100,000 cents.
    (n-1)Log3 = Log100,000,
    n-1 = Log100,000 / Log3 = 10.5,
    n = 11.5 years of age.

    b. A = 3^(18-1),
    A = 3^17 = 129,140,163 cents,
    A = $1,291,401.63.

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