Homework Help is Here – Start Your Trial Now!
Math
Calculus
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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
See similar textbooks
icon
Related questions
Question
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,
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS