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forum.virtualchallengemeets.com • View topic - Question

Question

I can do anything, as long as I have my handy-dandy Calculator.

Question

Postby ENHSmath » Thu Feb 07, 2013 4:52 pm

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
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Re: Question

Postby Shawn » Thu Feb 07, 2013 5:37 pm

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.
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
Y is uninfected so 1-y is infected
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
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