A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient- broth medium divides into two cells every 20 minutes. The initial population of a culture is 40 cells. (a) Find the relative growth rate. k= 3 ln (2) hr-1 (b) Find an expression for the number of cells after t hours. 40(231) P(t) = (c) Find the number of cells after 3 hours. 20480 cells (d) Find the rate of growth after 3 hours. (Round your answer to the nearest integer.) 42587 cells/h (e) When will the population reach a million cells? (Round your answer to two decimal places.) 5.98 h
A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient- broth medium divides into two cells every 20 minutes. The initial population of a culture is 40 cells. (a) Find the relative growth rate. k= 3 ln (2) hr-1 (b) Find an expression for the number of cells after t hours. 40(231) P(t) = (c) Find the number of cells after 3 hours. 20480 cells (d) Find the rate of growth after 3 hours. (Round your answer to the nearest integer.) 42587 cells/h (e) When will the population reach a million cells? (Round your answer to two decimal places.) 5.98 h
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-
broth medium divides into two cells every 20 minutes. The initial population of a culture is 40 cells.
(a) Find the relative growth rate.
k = 3 ln(2)
(b) Find an expression for the number of cells after t hours.
40(2³t)
P(t) =
hr-1
=
(c) Find the number of cells after 3 hours.
20480
cells
(d) Find the rate of growth after 3 hours. (Round your answer to the nearest integer.)
42587
cells/h
(e) When will the population reach a million cells? (Round your answer to two decimal places.)
5.98
h
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how did you divide 1million by 4 and get 250,000 it should be 25,000
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