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2. A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to

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2. A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 390. (a) (10 points) Find an expression for the number of bacteria after t hours. (b) (4 points) Find the number of bacteria after 3 hours. (You do not need to simplify). (c) (4 points) Find the rate of growth after 3 hours. (You do not need to simplify)

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