Problem 5: Osteoporosis in Chinese women (5 pts) The variations in age-related s

Question

Problem 5: Osteoporosis in Chinese women (5 pts) The variations in age-related speed of sound (SOS) at the tibia and the prevalence of osteoporosis in native Chinese women have been studied. They obtained the following relationship between the SOS and the age in years Y: sos 3383 +39.9Y - 0.78Y2 +0.0039y3 where the SOS is expressed in units of m/s. The SOS for one research subject is measured to be 3850 m/s. Use a numerical method to determine her most likely age. Take Y 45 years as your initial guess

Explanation / Answer

% I am using newton raphson method to solve the following problem.

% inputs

initialGuess=45;

tolerance=1e-8;

% function

f=@(x) 0.0039*x^3-0.78*x^2+39.9*x-467;

% iterations

iterations=1;

maximumIterations=1000;

d=@(x) 3*0.0039*x^2-2*0.78*x+39.9;

x(1)=initialGuess;

error=100;

while error>tolerance

x(iterations+1)=x(iterations)-((f(x(iterations))/d(x(iterations))));

error=abs((x(iterations+1)-x(iterations))/x(iterations));

  

iterations=iterations+1;

if(iterations==maximumIterations)

break;

end

end

root=round(x(iterations));

fprintf('Her most likely age: %d ', root);

% The output is coming as 57

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