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precalculas

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the amount of bacteria in a petri dish increased by a percent change of 12% each hour over a period of 15 hours.

a. find the growth factor for 1 hour?
b. by what total percent did the bacteria change during this 15- hour time period.?
c. how long will it take for the bacteria to double?

  • precalculus - ,

    a. 1.12

    b. [(1.12)^15 -1] x 100
    The x 100 is for conversion %

    c. about 6 hours, using the "rule of 72"

    For the exact answer (t), solve
    (1.12)^t = 2

  • precalculas - ,

    your formula would be
    Amount = a(1.12)^t , where 0 ≤ t ≤ 15

    a) in 1 hour growth factor would be 1.12
    b) Amount = a(1.12)^15 = 5.47a
    percentage of growth = 5.47a/a = 5.47 or 547%

    c)
    2a = a(1.12)^t
    2 = 1.12^t
    log2 = log(1.12^t)
    log2 = t log1.12
    t = log2/log1.12 = 6.1

  • precalculas - ,

    I do not agree with Reiny's answer #2. They asked for the change, so 1 must be subtracted from 1.12^15

    This would result in a 447% increase, to 547% of the initial value

  • precalculas - ,

    drwls is correct, I should have subtracted to get the change.

    (Can I blame it on the fact that I was only on my first cup of coffee ?)

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