Statement of a problem № 11245


One day, a cell phone company sends a text message to each of its 5800 subscribers, announcing that they have been automatically enrolled as contestants in a promotional lottery modeled on nuclear decay. On the first day, 10% of the 5800 contestants are notified by text message that they have been randomly eliminated from the lottery. The other 90% of the contestants automatically advance to the next round. On each of the following days, 10% of the remaining contestants are randomly eliminated, until fewer than 10 contestants remain. Determine (a) The activity (number of contestants eliminated per day) on the second day of the lottery, (b) The decay constant (in d-1) of the lottery, (c) The half-life (in d) of the lottery.

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