Approximately 14,000 bacteria are placed in a culture. Let P(t) be the number of bacteria present in the culture after t hours, and suppose that P(t) satisfies the differential eguation P'(t) = 0.55P(t) (a) Find the formula for P(t). P(t) = 14000e 55t (b) What is P(0)? (Give an exact answer.) P(0) = 14000 (c) How many bacteria are there after 6 hours? (Give your answer correct to the nearest integer.) 379577 bacteria (d) What is the growth constant? (Give an exact answer.) 55 (e) Use the differential equation to determine how fast the bacterla culture is growing when it reaches 140,000, (Give your answer correct to the nearest integer.) 77000 bacteria per hour (F) What is the size of the bacteria culture when it is growing at the rate of 55,000 bacteria per hour? (Glve your answer correct to the near est integer.) bacteria

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