Mrs Smith pays kate for babysitting by giving her 10 cents for the first-half hour, 20 cents for the second half-hour, 40 cents for the third half-hour etc. How long does she work to earn $12.70?

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  1. 1st half-hr = 10 cents = 5*2^1.

    2nd half-hr = 20 cents = 5*2^2.

    3rd half-hr = 40 cents = 5*2^3.

    t = 5*2^n = 1270 cents.
    5*2^n = 1270,
    Divide both sides by 5:
    2^n = 254,
    nlog2 = log254,
    n = log254 / log2 = 7.99 half-hrs =
    3.99 hrs or 4 hrs.

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