The specific growth rate g [day1 of a yeast bacterial culture that produces an a

Question

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 higlh 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. Note: The derivative of g(c) is 10(20 - 5c2 - 2c3) (c + 5)2 (c2 + 4)2

Explanation / Answer

CODE:

clc;

clear all;

close all;

count = 1;

for c = 0:.01:10

g(count) = 2*c/(4 + 0.8*c + c^2 + 0.2 * c^3);

cc(count) = c;

count = count + 1;

end

plot(cc,g)

xlabel('c')

ylabel('g')

fun = @(x) - (2*x./(4 + 0.8* x + x.^2 + 0.2. * x. ^ 3));

x1 = 0

x2 = 10;

options = optimset('Display,"iter');

[x,fval] = fminbnd(fun,x1,x2)

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