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A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into a nutrient broth, the culture grows at a rate proportional to its size. After 1.5 hours, the population has increased to 925.
(a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.)
P(1)-
(b) Find the number of bacteria after 5 hours. (Round your answer to the nearest whole number.)
P(S)-
bacteria
(c) Find the rate of growth (in bacteria per hour) after 5 hours. (Round your answer to the nearest whole number.)
P'(5)-
bacteria per hour
(d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.)
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