Question: Q6(20 points)Bacteria Growth.(a) During a fermentation experiment, the population P(t)(in millions per mL)of bacteriaLactobacillus plantarum after t hours in a malt medium satisfied the differential

Q6(20 points)Bacteria Growth.(a) During a fermentation experiment, the population P(t)(in millions per mL)of bacteriaLactobacillus plantarum after t hours in a malt medium satisfied the differential equationdPdt=0.4P(1-P12,500)Initially, 9 million bacteria per mL were present.(i) Determine the number of bacteria per mL after 7 hours.(ii) Determine when 900 million bacteria per mL will be present.(b) During a fermentation experiment, the population P(t)(in millions per mL)of bacteriaLactobacillus fermentum after t hours in a wheat medium satisfied the differential equationdPdt=0.532P(1-P1900)Initially, 8 million bacteria per mL were present.(i) Calculate P(1) using Euler's method with a step size ofh=0.2hr.(ii) Calculate P(1) using the exact solution.

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