During a flu epidemic in a city of 1,000,000, a flu vaccine sells in proportion to...

During a flu epidemic in a city of 1,000,000, a flu vaccine sells in proportion to both the number of people already inoculated and the number not yet inoculated. If 100 doses have been sold at time t = 0and after 5 weeks 8000 doses have been sold, find a formula for the total number of doses sold within t weeks.

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