A microbiologist is testing an enzyme suspected to reduce the growth rate of a certain type of bacteria, and she wants t write a piecewise function to describe the effect she observes. She notices there is not a decrease in the size of the culture after the solution is applied, but that the growth rate decreases following its application. She is monitoring the changing mass of the culture because it is not practical to count individual cells, and she wants to model this with a continuous function representing the mass M (t) after t hours, made up of two exponential growth functions of the form M (t) = aekt. The bacteria culture is known to follow the growth model M (t) = 50e-032t for an initial sample of 50 grams. She allow the culture to grow unchecked for 48 hours before adding the experimental enzyme. She then finds that the mass of the culture 48 hours after application of the enzyme is about 546 grams. Use the limit definition of continuity to solve for the values of a and k that make the function continuous. 50e-032t, 0 < t < 48 t> 48 M(t) = {ackt, Don't forget to tell the story of your ght process, how you choose the calculations you do! Describe how you choose each limit computation, how you know it will create a function which is continuous. Guiding Discussion Questions: • What does the graph of this function look like? How can this help us understand what we're solving for? • How is two-sided continuity related to continuity on each side? • Is this function already guaranteed to be continuous on one side? If so, left or right? How do we know? • What is the equation (involving limits) corresponding to continuity on the other side? • What resources can help us review if we're having a hard time solving the equation to make the function continuous?
A microbiologist is testing an enzyme suspected to reduce the growth rate of a certain type of bacteria, and she wants t write a piecewise function to describe the effect she observes. She notices there is not a decrease in the size of the culture after the solution is applied, but that the growth rate decreases following its application. She is monitoring the changing mass of the culture because it is not practical to count individual cells, and she wants to model this with a continuous function representing the mass M (t) after t hours, made up of two exponential growth functions of the form M (t) = aekt. The bacteria culture is known to follow the growth model M (t) = 50e-032t for an initial sample of 50 grams. She allow the culture to grow unchecked for 48 hours before adding the experimental enzyme. She then finds that the mass of the culture 48 hours after application of the enzyme is about 546 grams. Use the limit definition of continuity to solve for the values of a and k that make the function continuous. 50e-032t, 0 < t < 48 t> 48 M(t) = {ackt, Don't forget to tell the story of your ght process, how you choose the calculations you do! Describe how you choose each limit computation, how you know it will create a function which is continuous. Guiding Discussion Questions: • What does the graph of this function look like? How can this help us understand what we're solving for? • How is two-sided continuity related to continuity on each side? • Is this function already guaranteed to be continuous on one side? If so, left or right? How do we know? • What is the equation (involving limits) corresponding to continuity on the other side? • What resources can help us review if we're having a hard time solving the equation to make the function continuous?
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
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![**Application - Biology**
A microbiologist is testing an enzyme suspected to reduce the growth rate of a certain type of bacteria, and she wants to write a piecewise function to describe the effect she observes. She notices there is not a decrease in the size of the culture after the solution is applied, but that the growth rate decreases following its application. She is monitoring the changing mass of the culture because it is not practical to count individual cells, and she wants to model this with a continuous function representing the mass \( M(t) \) after \( t \) hours, made up of two exponential growth functions of the form \( M(t) = a e^{k t} \).
The bacteria culture is known to follow the growth model \( M(t) = 50 e^{.032 t} \) for an initial sample of 50 grams. She allows the culture to grow unchecked for 48 hours before adding the experimental enzyme. She then finds that the mass of the culture 48 hours after application of the enzyme is about 546 grams.
Use the limit definition of continuity to solve for the values of \( a \) and \( k \) that make the function continuous.
\[ M(t) = \begin{cases}
50 e^{.032 t}, & 0 \le t < 48 \\
a e^{k t}, & t \ge 48
\end{cases} \]
Don't forget to tell the story of your thought process, how you choose the calculations you do! Describe how you choose each limit computation, how you know it will create a function which is continuous.
**Guiding Discussion Questions:**
- What does the graph of this function look like? How can this help us understand what we're solving for?
- How is two-sided continuity related to continuity on each side?
- Is this function already guaranteed to be continuous on one side? If so, left or right? How do we know?
- What is the equation (involving limits) corresponding to continuity on the other side?
- What resources can help us review if we're having a hard time solving the equation to make the function continuous?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36ade1a1-f50c-49e6-9973-e1b61dc80212%2F301f6dd1-96ab-48e0-aec7-a353f5567f49%2F3gacjp3i_processed.png&w=3840&q=75)
Transcribed Image Text:**Application - Biology**
A microbiologist is testing an enzyme suspected to reduce the growth rate of a certain type of bacteria, and she wants to write a piecewise function to describe the effect she observes. She notices there is not a decrease in the size of the culture after the solution is applied, but that the growth rate decreases following its application. She is monitoring the changing mass of the culture because it is not practical to count individual cells, and she wants to model this with a continuous function representing the mass \( M(t) \) after \( t \) hours, made up of two exponential growth functions of the form \( M(t) = a e^{k t} \).
The bacteria culture is known to follow the growth model \( M(t) = 50 e^{.032 t} \) for an initial sample of 50 grams. She allows the culture to grow unchecked for 48 hours before adding the experimental enzyme. She then finds that the mass of the culture 48 hours after application of the enzyme is about 546 grams.
Use the limit definition of continuity to solve for the values of \( a \) and \( k \) that make the function continuous.
\[ M(t) = \begin{cases}
50 e^{.032 t}, & 0 \le t < 48 \\
a e^{k t}, & t \ge 48
\end{cases} \]
Don't forget to tell the story of your thought process, how you choose the calculations you do! Describe how you choose each limit computation, how you know it will create a function which is continuous.
**Guiding Discussion Questions:**
- What does the graph of this function look like? How can this help us understand what we're solving for?
- How is two-sided continuity related to continuity on each side?
- Is this function already guaranteed to be continuous on one side? If so, left or right? How do we know?
- What is the equation (involving limits) corresponding to continuity on the other side?
- What resources can help us review if we're having a hard time solving the equation to make the function continuous?
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