Differential Equation - Blood Alcohol

Question

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.

Answer 1

And the solution is $$\frac{dC(t)}{dt}=-\alpha C(t)$$ where $\alpha \gt 0$. Solving the equation we have $$C(t)=C(0)\exp{(-\alpha t)}$$