Science:Math Exam Resources/Courses/MATH103/April 2005/Question 07 (b)

MATH103 April 2005

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Question 07 (b)

Cholera is a disease that can spread through untreated sewage polluting the drinking water supply. Let $\displaystyle y(t)$ be the fraction of people in a population who have the disease at time t. Assume that in a certain city, the fraction of people who have the disease increases at a rate proportional to the fraction of people who do not yet have the disease. (We will use $\displaystyle k>0$ as the constant of proportionality). (b) Solve this differential equation, assuming that at time $\displaystyle t=0$ the fraction of people who have the disease is $\displaystyle y(0)=y_{0}$ where $\displaystyle 0\leq y_{0}\leq 1$

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Hint

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