Question

Part A (Based off week 2 Workshop content) Sam, a biological engineer, is modelling the population of bacteria (B) grow ing on petri dish. Sam observes that the growth over time of the bacteria fits the equation Cert B(t) = 1. (AMS Submission) Write a MATLAB function that accepts four inputs C, r, K and t and outputs bacteria population. The function should work given t is a scalar or a vector. You may assume that all other inputs are scalars. 2, (AMS Submission) By setting r = 1, C = 100 and t = 0 : 20, plot 5000. What the bacteria growth for K- 1000, K 3000, and K - does K represent? 3. Sam starts with 500 bacteria in his petri dish. Seven days later, the number of cells has doubled. Given that the petri dish can support a maximum of 9000 cells, calculate the values of C, r and K. Plot the solution and comment whether the plot matches Sam's observations 4. (AMS Submission) Assume that each time bacteria is grown, Sam records the initial bacteria population, the time it takes for the initial population to double, and the final (maximum) population. Create a function that will tell Sam the values of C, r and K

Please help - i dont know how to solved these

Answer 1

copyable code:

MATLAB Code:

%function definition for population of bacteria

function B = bacteriaFunction(C,r,K,t)

%compute B(t)

B = C*exp(r*t)./(1+C/K*exp(r*t));

%plot the t and B(t)

plot(t,B)

%label for x-axis

xlabel('t');

%label for y-axis

ylabel('B(t)');

hold on

end

%call given function

B = bacteriaFunction(100,1,1000,0:20)

MATLAB Code:

%function definition for population of bacteria

function B = bacteriaFunction(C,r,K,t)

%compute B(t)

B = C*exp(r*t)./(1+C/K*exp(r*t));

%plot the t and B(t)

plot(t,B)

%label for x-axis

xlabel('t');

%label for y-axis

ylabel('B(t)');

hold on

end

t = linspace(0,20,101);

r = 1;

C = 100;

K = 1000;

%call given function

bacteriaFunction(C,r,K,t);

K = 3000;

%call given function

bacteriaFunction(C,r,K,t);

t = linspace(0,20,101);

r = 1;

C = 100;

K = 5000;

%call given function

bacteriaFunction(C,r,K,t);

legend('K=1000','K=3000','K=5000')

%function definition for double population

function [C,r] = bacteriaDoubleFunction(B,K,tn)

%compute C value

C = B*K/(K-B);

%compute r value

r = 1/tn*log(2*B/(C-2*B*C/K));

end

%call function

[C,r] = bacteriaDoubleFunction(500,9000,7)