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 775. (a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.) P(t) = 50(6.2166) (b) Find the number of bacteria after 5 hours. (Round your answer to the nearest whole number.) P(5) = 311 bacteria (c) Find the rate of growth (in bacteria per hour) after 5 hours. (Round your answer to the nearest whole number.) P'(5)= 841500 bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.) t = hr

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