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In a large population , the rate at which a disease spreads is proportional to the number of uninfected people. If one person catches a cold, and 5 days later, 25% of the population is sick, what fraction of the population is sick when the first person recovers from their cold? Assume a cold lasts 12 days.

Answer 49.9

This is an example, where problem identification is helpful. Since it gives you a condition at one time and asks for what it is at another time, it probably involves exponential growth/decay. Below is the decay setup. There is probably a quicker way to do this kind of problem.
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Y is uninfected so 1-y is infected
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