A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 240. (a) Find an expression for the number of bacteria after t hours. P(t) = (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.) P(2) = bacteria (c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.) P'(2) = bacteria per hour (d) When will the population reach 10,000? (Round your answer to one decimal place.) hr

Question
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 240.
(a) Find an expression for the number of bacteria after t hours.
P(t) =
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.)
P(2) =
bacteria
(c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.)
P'(2) =
bacteria per hour
(d) When will the population reach 10,000? (Round your answer to one decimal place.)
hr
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Transcribed Image Text

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 240. (a) Find an expression for the number of bacteria after t hours. P(t) = (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.) P(2) = bacteria (c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.) P'(2) = bacteria per hour (d) When will the population reach 10,000? (Round your answer to one decimal place.) hr

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