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, xu-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.

Systems Architecture
7th Edition
ISBN:9781305080195
Author:Stephen D. Burd
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Chapter12: Secondary Storage Management
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The specific growth rate g [day¹] 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, xu-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.
Transcribed Image Text:The specific growth rate g [day¹] 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, xu-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.
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