Anonymous asked in Science & MathematicsMathematics · 5 months ago

How many days will it take for the fruit flies population to be double, if the rate of growth in a population of fruit flies is 10% per day?

1 Answer

  • 5 months ago
    Favorite Answer

    If there is a 10% increase per day, then we can set up this equation:

    a(t) = a(1.1)^t

    Where "a" is the starting population

    a(t) is the population after "t" days

    t is the number of days

    It doesn't matter what "a" is as long as we double it, then we can solve for t.  So let's set:

    a = 1

    a(t) = 2

    Then solve for t:

    a(t) = a(1.1)^t

    2 = 1(1.1)^t

    2 = (1.1)^t

    ln(2) = ln[(1.1)^t]

    ln(2) = t ln(1.1)

    ln(2) / ln(1.1) = t

    That's the exact answer.  A decimal approximation is:

    t = 7.27 days (rounded to 2DP)

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