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Calc 2 college

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Modeling with differential equations.
If a bacteria culture doubles every 10 minutes and the original culture has 300 cells determine the rate of growth.

  • Calc 2 college -

    y = c e^kt

    dy/dt = k c e^kt = k y

    when t = 0 e^kt = e^0 = 1
    y(0) = c

    so
    y = 300 e^kt
    when t = 10
    y = 600
    600 = 300 e^10k
    2 = e^10 k
    ln 2 = 10 k
    k = .0693/minute

  • Calc 2 college -

    Thanks

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