The bacterium Streptococcus pyogenes (S. pyogenes) is the cause of many human diseases, the most common being strep throat. The doubling time of these bacteria is 30minutes, but in the presence of a certain antibiotic the doubling time is 6 hours. Two cultures are prepared, and the antibiotic is added to one of the cultures. Initially, eachculture has 200 bacteria.(a) Find an exponential model for the number of S. pyogenes bacteria in each culture after t hours.fno antibiotic(t)bacteriafwith antibiotic(t)bacteria (b) Graph the models for t between 0 and 8.f(t)f(t)1200120010001000800antibiotic800antibiotic600600400400no antibioticno antibiotic200200248246.8f(t)f(t)1200120010001000800no antibiotic800no antibiotic600600400400antibioticantibiotic200200t8846.What do the graphs tell us about the number of bacteria?The culture with the antibiotic grows much more rapidly.The culture without the antibiotic grows much more rapidly.(c) For each model, find the predicted number of bacteria after 8 hours. (Round your answers to the nearest whole number.)fno antibiotic(8)bacteria%3Dfwith antibiotic(8)bacteria

The bacterium Streptococcus pyogenes (S. pyogenes) is the cause of many human diseases, the most common being strep throat. The doubling time of these bacteria is 30 minutes, but in the presence of a certain antibiotic the doubling time is 6 hours. Two cultures are prepared, and the antibiotic is added to one of the cultures. Initially, each culture has 200 bacteria. (a) Find an exponential model for the number of S. pyogenes bacteria in each culture after t hours. fno antibiotic(t) = bacteria fwith antibiotic(t) = bacteria

The bacterium Streptococcus pyogenes (S. pyogenes) is the cause of many human diseases, the most common being strep throat. The doubling time of these bacteria is 30 minutes, but in the presence of a certain antibiotic the doubling time is 6 hours. Two cultures are prepared, and the antibiotic is added to one of the cultures. Initially, each culture has 200 bacteria. (a) Find an exponential model for the number of S. pyogenes bacteria in each culture after t hours. fno antibiotic(t) = bacteria fwith antibiotic(t) = bacteria

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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The bacterium Streptococcus pyogenes (S. pyogenes) is the cause of many human diseases, the most common being strep throat. The doubling time of these bacteria is 30
minutes, but in the presence of a certain antibiotic the doubling time is 6 hours. Two cultures are prepared, and the antibiotic is added to one of the cultures. Initially, each
culture has 200 bacteria.
(a) Find an exponential model for the number of S. pyogenes bacteria in each culture after t hours.
fno antibiotic(t)
bacteria
fwith antibiotic(t)
bacteria

(b) Graph the models for t between 0 and 8.
f(t)
f(t)
1200
1200
1000
1000
800
antibiotic
800
antibiotic
600
600
400
400
no antibiotic
no antibiotic
200
200
2
4
8
2
4
6.
8
f(t)
f(t)
1200
1200
1000
1000
800
no antibiotic
800
no antibiotic
600
600
400
400
antibiotic
antibiotic
200
200
t
8
8
4
6.
What do the graphs tell us about the number of bacteria?
The culture with the antibiotic grows much more rapidly.
The culture without the antibiotic grows much more rapidly.
(c) For each model, find the predicted number of bacteria after 8 hours. (Round your answers to the nearest whole number.)
fno antibiotic(8)
bacteria
%3D
fwith antibiotic(8)
bacteria

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