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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) aft 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-032r 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. S 50e.0321, 0 48

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) aft 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-032r 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. S 50e.0321, 0 48

Calculus: Early Transcendentals
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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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) aft t hours, made up of two exponential growth functions of the form M (t) = aek. The bacteria culture is known to follow the growth model M (t) = 50e.032r 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. .032t 0 <t < 48 t > 48 M(t) = aekt,
Transcribed Image Text: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) aft t hours, made up of two exponential growth functions of the form M (t) = aek. The bacteria culture is known to follow the growth model M (t) = 50e.032r 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. .032t 0 <t < 48 t > 48 M(t) = aekt,
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