Nie 發問於 科學及數學數學 · 5 年前

Math, basic differentiation?

I am really bad in math, would you please help?

The number of bacteria B(t) in a certain culture t min after an experimental bactericide is introduced obeys the formula: B(t)=(10000/(1+t^2))+500. Find the rate of change of the number of bacteria in the culture 1 min and 2 min after the bactericide is introduced.

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    B(t) = 10000/(1 + t²) + 500

    The rate of change of the number of bacteria

    = B'(t)

    = [10000/(1 + t²) + 500]'

    = [10000(1 + t²)⁻¹]'  ..........  [C]' = dC/dt = 0 where C is a constant

    = -10000(1 + t²)⁻¹⁻¹ (1 + t²)'  ..........  ( Chain Rule )

    = -10000/(1 + t²)² (2t)

    = -20000t/(1 + t²)²

    The rate of change of the number of bacteria in the culture 1 min

    = B'(1)

    = -20000(1)/[1 + (1)]²

    = -5000

    The rate of change of the number of bacteria in the culture 1 min

    = B'(2)

    = -20000(2)/[1 + (2)]²

    = -40000/9

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