Let C(t) be the concentration of alcohol in a person's bloodstream. We propose a mathematical model which states that, once a person stops drinking alcohol, C decreases at a rate that is proportional to C. Write down a differential equation consistent with that model.
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Hint: the rate of decrease is the derivative of $C$ and is negative when the concentration is positive – marwalix Feb 06 '15 at 10:06
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Another Hint: saying that a function $f$ is proportional to a function $g$ means that there exists some $\alpha \in \Bbb{R}$ such that $f=\alpha g$. Next look at @marwalix solution, if you don't get it by yourself :D – Bman72 Feb 06 '15 at 10:27
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And the solution is $$\frac{dC(t)}{dt}=-\alpha C(t)$$ where $\alpha \gt 0$. Solving the equation we have $$C(t)=C(0)\exp{(-\alpha t)}$$
marwalix
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Are you sure? At $t=0$ your solution is $0$! So the person is sober. :-) – vanguard2k Feb 06 '15 at 10:17
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