# 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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