The specific growth rate g [day] of a yeast bacterial culture that produces an antibiotic is a function of food concentration, c [mg/L] according to g(c) = 2c 4+0.8c + c² + 0.2c³ Growth goes to zero at very low concentration due to food limitation. It also goes to zero at high concentration due to toxicity effects. Write an m-file to determine the value of c at which the growth is maximum using the false position method. For your calculation use an initial guess of x=0 mg/L, x,-5 mg/L and a precision of 1e-4. Plot the following three graphs in one figure to verify that your answer is correct. Ensure you label your plots. Plot g against c, where c ranges from 0 to 10. Plot the derivative of g against c for the same range above. • Plot a vertical line at the solution found by false position method Write a statement which describes the value of the concentration when the growth is a maximum, and the number of iterations it took to obtain the value. Note: The derivative of g(c) is g'(c): 10(20-5c²-2c³) (c + 5)²(c²+4)²

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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The specific growth rate g [day'¹] of a yeast bacterial culture that produces an antibiotic is a function
of food concentration, c [mg/L] according to
g(c):
Growth goes to zero at very low concentration due to food limitation. It also goes to zero at high
concentration due to toxicity effects.
2c
4+0.8c+ c² + 0.2c³
Write an m-file to determine the value of c at which the growth is maximum using the false position
method. For your calculation use an initial guess of x=0 mg/L, x,-5 mg/L and a precision of 1e-4. Plot
the following three graphs in one figure to verify that your answer is correct. Ensure you label your
plots.
●
Plot g against c, where c ranges from 0 to 10.
Plot the derivative of g against c for the same range above.
•
Plot a vertical line at the solution found by false position method
Write a statement which describes the value of the concentration when the growth is a maximum,
and the number of iterations it took to obtain the value.
Note: The derivative of g(c) is
g'(c)
10(20-5c²2c³)
(c + 5)² (c² + 4)²
Transcribed Image Text:The specific growth rate g [day'¹] of a yeast bacterial culture that produces an antibiotic is a function of food concentration, c [mg/L] according to g(c): Growth goes to zero at very low concentration due to food limitation. It also goes to zero at high concentration due to toxicity effects. 2c 4+0.8c+ c² + 0.2c³ Write an m-file to determine the value of c at which the growth is maximum using the false position method. For your calculation use an initial guess of x=0 mg/L, x,-5 mg/L and a precision of 1e-4. Plot the following three graphs in one figure to verify that your answer is correct. Ensure you label your plots. ● Plot g against c, where c ranges from 0 to 10. Plot the derivative of g against c for the same range above. • Plot a vertical line at the solution found by false position method Write a statement which describes the value of the concentration when the growth is a maximum, and the number of iterations it took to obtain the value. Note: The derivative of g(c) is g'(c) 10(20-5c²2c³) (c + 5)² (c² + 4)²
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