Growth data of a sunflower plant is given in the following table: The data can b

Question

Growth data of a sunflower plant is given in the following table: The data can be modeled with a function in the form H = C/(1 +Ae^-Br) (logistic equation), where H is the height, C is a maximum value for H, A and B are constants, and t is the number of weeks. By using the method described in Section 8.2.2, and assuming that C = 254 cm, determine the constants A and B such that the function best fit the data. Use the function to estimate the height in week 6. In one figure, plot the function and the data points.

Explanation / Answer

% start the script

X= [1 3 5 7 9 11 13];

H= [22 51 127 202 227 248 252];

Y= [10.5454 3.9804 10.2574 0.1189 0.0242 0.0079];

C=254;

P=polyfit(x, log(y), 1);

A=exp (p (2))

B=-p (1)

X1= [1:1:13];

H1=c. / (1+A*exp (-B*x1));

Fprintf (‘the height in cm in week 6 =%6.2f ’, c/ (1+A*exp (-B*6)))

Plot (x, H,’0’)

Hold on

Plot(x1, h1)

Title (‘height vs number of weeks ‘)

Xlabel (‘t (weeks)’);

Ylabel (‘height (cm)’);

The mat lab output :

A=21.1829

B=0.6058

The height in week 6=162.92cm

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