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calculus

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Pretend the program in Senegal had been reducing infant mortality at a rate
of 12.2 % per year. How long would it take for infant mortality
to be reduced by 31 %?

  • calculus - ,

    100 - 12.2 = 87.8%

    dx/dt = -.122 x

    dx/x = -.122 dt

    ln x = -.122 t + C

    x = e^(C-.122 t)

    x = c e^(-.122 t)
    when t = 0, x = 100%
    so
    x = 100 % e^(-.122 t)
    (100 %-31 %) = 100 % e^-.122 t
    .69 = e^(-.122 t)
    ln(.69) = -.122 t
    -.371 = -.122 t
    t = 3.04 years

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