The growth rate of Escherichia coli, a common bacterium found in the human intes
ID: 3083847 • Letter: T
Question
The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 15 min.
(a)If the initial population is 10, determine the function Q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes). Answer: Q(t)=10e^[ln(2)/15]
(b)How long would it take for a colony of 10 cells to increase to a population of 1 million? (Round your answer to the nearest whole number.) Answer:_____________
Explanation / Answer
let Q(t) = Aet
As it Double its No. in 15 min
Threfore
t = ln(2)/ = 15
= ln(2)/15
Therefore
Q(t) = Ae[ ln(2)/15 ]t
Also
at t = 0 , Q(0) = 10
Therefore
A = 10
Therefore
Q(t) = 10e[ ln(2)/15 ]t
=======================
Q(t) = 10e[ ln(2)/15 ]
10^6 = 10e[ ln(2)/15 ]t
Therefore
t = 249.144 min
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