# Math - Exponential

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Suppose the % of alc. in the blood, t, hours after consumption is C(t) = 0.3te^(-t/2). How much time passes before the blood alcohol lvl starts to decrease?

C'(t) = 0.3e^(-t/2) - 0.15te^(-t/2)
C'(t) = e^(-t/2)(0.3 - 0.15t)
0 = 0.3 - 0.15t
t = 2 hours

So... 2 hours passes before it starts to decrease

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Records show that, t, weeks after the outbreak of a specific disease, approx. Q(t) = 15/(1 + 14e^(-1.7t)) thousand people had caught it. If the trend continues, approx. how many people will eventually contract it?

Q(0) = 15/1
Q(0) - 15 000

So... 15,000 people will contract the disease.

• Math - Exponential -

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