Question

The table below contains data from an experiment to determine the growth rate of bacteria, k, as a function of oxygen concentration, c:

c (mg/L) 0.5 0.8 1.5 2.5 4

k (per day) 1.1 2.4 5.3 7.6 8.9

A) Fit this data to a curve of the form:k =(Ac^2)/(B+c^2) Make sure to display and identify the values you get for A and B. Hint: transform the curve in c and k to a polynomial in (1/c2) and (1/k)

B) Plot the data points and the approximating function over the range c = 0 to 4.5 on a single figure. Use diamonds to represent the data points, a green dashed line for the approximating curve.

C) Estimate the growth rate at c = 2 mg/L using your approximating function.

Answer 1

Answer: Note: All parts are answered. Given: Given curve form, Now linearize the equation, 1 k A. Let us take, y (1/k), x-(1/ c2), Therefore, y aix + ao ao (IA) and a,-(B/A) MATLAB code: %Part A) Define function to find the A and B value function [A, B] = findABValue (c, k) %initialize the output to 0 A0; B0; %Find the length of the data points n - length (c); %Create new array to store 1/c^2 csqzeros (n, 1);

%create new array to store 1/k ksqzeros (n, 1); %Declare variable of (1/c^2 1/k) to store sum * sumCK = 0 ; %Declare variable of (1/c^2 1/c^2) to store sum * sumtp0 %Loop for aa-1: rn %Find current 1/c^2 %Find 1/k ksq(aa) 1/k (aa); = %Update sum sumCK Csq (aa) * ksq (aa) %Update sum End of for loop end

c = [ 0.5 0.8 1.5 2.5 4); %Define k k[1.1 2.4 5.3 7.6 8.91 %Call function to find A and B [A, BfindABValue (c, k) %Print A value fprintf ( ' \nA value : %1 ' , A) ; %Print B value fprintf ( ' \nB value : %1\n', B); %Part B) 8Define c range CAry = 0:0.5:4.5; %create K array KAryzeros (length (CAry), 1); 100p t find K value for kk -1:length (CAry) Get present c value cval = CAry (kk) ;

%Find k newK - 1/ (B/ (A newc2) (1/ A)); 8Display k value for the given c value fprintf('\n\nFor c= 2 mg/L, the growth rate: %.4f', newK); Sample Output: A value: 10.0607 B value: 2.03719 10 - 4. Data point:s Approximatting Function 4 For c2 mg/L, the growth rate: 6.6658