A common inhabitant of human intestines is the bacterium Escherichia coli . A ce
ID: 2849007 • Letter: A
Question
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 69 cells.
(a) Find the relative growth rate. (Assume t is measured in hours.)
k =
(b) Find an expression for the number of cells after t hours.
P(t) =
(c) Find the number of cells after 8 hours.
cells
(d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.)
billion cells per hour
(e) When will the population reach 20,000 cells? (Round your answer to two decimal places.)
hr
Explanation / Answer
The number of bacteria at any time t, in hours is p(t)=Ae^(kt)
you know A when t=0 is 69
e^(kt)=2 at t=1/3 hours or 20 minutes take ln in each side
ln(2)=k(0.33)=0.6933
k=2.08
After t hours
p(t)=69e^(2.08)t
After 8 hours
p(8)=69e^(2.08)(8)=4418.46
The rate of growth at 8 hours is still e^(2.08)t doubling every 20 min
p(t)=20000=69e^(2.08)t ln in each of the side
289.85=e^(2.08)t
5.669=(2.08)t
t=2.725 hours
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