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A town has 100 people infected with a particular cold at the beginning of the year....

A town has 100 people infected with a particular cold at the beginning of the year. It is estimated that every week each infected person infects three others, but recovers from the cold. Let in be the number of people infected after week n (measured from the beginning of the year). How long will it be before at least 60000 people are infected?

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