Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

The size of an exponentially growing bacteria colony doubles in 5 hours.?

How long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.

Exact:

Decimal (nearest hundreth):

3 Answers

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  • Faz
    Lv 7
    1 decade ago
    Favorite Answer

    Find the growth rate:

    2 = e^(5r)

    r = ln2 / 5

    To triple therefore, solve the following for t:

    3 = e^((ln2/5)t)

    t = 5ln(3) / ln(2) (exact)

    t = 7.92 hours (approx)

  • 4 years ago

    Exponentially Growing

  • 1 decade ago

    PN = PS(2^(t/5)) where PS is the population at start and PN is the population after t hours. Evaluate t, for PN = 3(PS)

    3(PS) = PS(2^(t/5))

    3 = 2^(t/5)

    log3 = log[2^(t/5)]

    log 3 = (t/5)log2

    (log3)/log2) = t/5

    5(log3)/(log2) = t

    There are no exact values for logs - most are irrational numbers.

    log(3) = 0.477121254...

    log(2) = 0.3010249995...

    t = 5(0.477121254...)/(0.3010249995...)

    = 7.924812504....

    = 7.92 hours to the nearest hundredth

    Source(s): Retired math teacher
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