Approximately 10,000 bacteria are placed in a culture. Let P(t) be the number of

Question

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: p'(t)=.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 for the bacteria culture when it is growing at a rate of 34,000 bacteria per hour?

Explanation / Answer

dp(t)/dt=0.55p(t) so integrating we get ln(p(t))=0.55t+c p(t)=ke^0.55t (a)p(0)=10000 (b)p(t)=10000e^0.55t (c)p(5)=156426 (d)growth constant=0.55 (e)0.55x100,000=55000 (f)34000=0.55xp p=61818

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