Approximately 10,000 bacteria are placed in a culture. Let P(t) be the number of bacteria present in
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Approximately 10,000 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 equation (t) = 0.55P(t).
(a) What is P(0)?
(b) Find the formula for P(t).
(c) How many bacteria are there after 5 hours?
(d) What is the growth constant?
(e) Use the differential equation to determine how fast the bacteria culture is growing when it reaches 100,000.
(f ) What is the size of the bacteria culture when it is growing at a rate of 34,000 bacteria per hour?
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