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

MATH103 April 2005

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### Question 07 (a)

Cholera is a disease that can spread through untreated sewage polluting the drinking water supply. Let ${\displaystyle \displaystyle y(t)}$ 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 ${\displaystyle \displaystyle k>0}$ as the constant of proportionality).

(a) Write down the differential equation that y(t) satisfies.

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