The value of pi can be estimated by squareroot 6sigmainfinit

The value of pi can be estimated by: squareroot 6(sigma^infinity_n = 1 1/n^2) Write a program (using a loop) that determines the expression. Run the program with n = 100, n = 10000, and n = 1000000. Compare the result with pi. (Use format long.) USING MAT LAB CODE: 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/(l +Ae^-Bt) (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.

Solution

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Enter the following MATLAB code:

x = [1 3 5 7 9 11 12 13]

H = [22 51 127 202 227 248 252]

y = [10.5454 3.9804 1 0.2574 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 week 6 = %6.2f\ \', C/(1+A*exp(-B*6)))

plot (x,H,\'o\')

hold on

plot(x1,H1)

title (\'Height vs Number of weeks\')

xlable(\'t (weeks)\');

ylable(\'Height (cm)\');

Output:

A = 21.1829

B = 0.6058

The height in week 6 = 162.92 cm