2. [-/4 Points] DETAILS SCALCET9 3.8.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 825. (a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.) P (t ) = (b) Find the number of bacteria after 7 hours. (Round your answer to the nearest whole number.) P(7) = bacteria (c) Find the rate of growth (in bacteria per hour) after 7 hours. (Round your answer to the nearest whole number.) P'(7) = bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.) t = hr