Approximately 15,000 bacteria are placed in a culture. Let P(t) be the number of

Question

Approximately 15,000 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) = 0.55P(t). Find the formula for P(t). P(t) = What is P(0)? (Give an exact answer.) P(0) = How many bacteria are there after 4 hours? (Give your answer correct to the nearest integer.) bacteria What is the growth constant? (Give an exact answer.) Use the differential equation to determine how fast the bacteria culture is growing when it reaches 150,000. (Give your answer correct to the nearest integer.) bacteria per hour What is the size of the bacteria culture when it is growing at the rate of 59,000 bacteria per hour? (Give your answer correct to the nearest integer.) bacteria

Explanation / Answer

Solution:

Given The Differential Equation

p'(t) = 0.55 p(t)

a)

Formula For P(t) = 15000 e(0.55t)

b)

p(0) = 15000

c)

At 4 hours

t = 4

P(4) = 15000 e(0.55*4)

= 15000 e2.2

= 15000*9.025

= 135,375

e)

p(t) = 150000

P '(t) = 0.55P(t)

= 0.55*150000

= 82,500 bacteria per hour

f)

p'(t) = 59,000

59000 = 0.55P(t)

P(t) = 59,000/0.55

= 107,272.727 bacteria

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