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A rumour is spreading in a nursing home which contains 100 pensioners. The rumour spreads at a rate proportional to both the number who have heard the rumour and the number who have not yet heard the rumour. At first, 4 pensioners in the home have heard the rumour, and after 2 weeks, 20 pensioners have heard it. How long is it before 50 pensioners in the home have heard the rumour?

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