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15 July, 20:32

You are staying at a hotel that has a hot tub. The quick forgot to make sure it was heated up. Right now the temperature is 70°. The clerk says it will get 10 percent warmer every hour. When will the temperature be at least 103°

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  1. 15 July, 20:38
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    This is a poorly worded problem.

    The problem should state that the water temperature in degrees F increases 10% each hour, not that the water is warmer by 10%.

    In any case, use exponential growth.

    F = P (1 + r) ^t

    103 = 70 (1 + 0.1) ^t

    Solve for t.

    1.1^t = 103/70

    log (1.1^t) = log (103/70)

    t * log 1.1 = log (103/70)

    t = (log (103/70)) / (log 1.1)

    t = 4.05

    The temperature will be at least 103 deg in 4.05 hours.
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