Growth of Bacteria 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 20 min. (a) If the initial population is 500, 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). Q(t)= 500e 0.0347t X (b) How long would it take for a colony of 500 cells to increase to a population of 1 million? (Round your answer to the nearest whole number.) 219.04 ✔min (c) If the initial cell population were 5000, what is our model? Q(t) = 50000.0347t X
Growth of Bacteria 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 20 min. (a) If the initial population is 500, 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). Q(t)= 500e 0.0347t X (b) How long would it take for a colony of 500 cells to increase to a population of 1 million? (Round your answer to the nearest whole number.) 219.04 ✔min (c) If the initial cell population were 5000, what is our model? Q(t) = 50000.0347t X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Need help
![Growth of Bacteria 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 20 min.
(a) If the initial population is 500, 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).
0.0347t
Q(t) = 500e
X
(b) How long would it take for a colony of 500 cells to increase to a population of 1 million? (Round your answer to the nearest whole number.)
219.04
min
(c) If the initial cell population were 5000, what is our model?
5000e0.0347t
Q(t) =
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ef2aea6-ca63-493c-95d5-a7314878e877%2F9e43ef21-fc2e-4d05-aa8b-1928669ec9a4%2F4bl1gva_processed.png&w=3840&q=75)
Transcribed Image Text:Growth of Bacteria 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 20 min.
(a) If the initial population is 500, 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).
0.0347t
Q(t) = 500e
X
(b) How long would it take for a colony of 500 cells to increase to a population of 1 million? (Round your answer to the nearest whole number.)
219.04
min
(c) If the initial cell population were 5000, what is our model?
5000e0.0347t
Q(t) =
X
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)