Question

Q3b In the Q3b.m file, plot the PFA against the year as blue circles in a new figure. You believe that the data can be appropriately represented by either an exponential model or a 2d order polynomial model. Find the coefficients for each model based on the form of the equations below: Exponential model: PFA- aeBt 2 order polynomial model: PFA at2 + bt + c where a. B, o, b, c are coefficients, and t represents the year Plot both fitted models for years 1950 to 2100 (yearly increments) on the newly created figure. Print the equations of the fitted models to the command window using the exponential specifier for fprintf *You should have six figure windows by the end of this task

Answer 1

Code:

t = [1950 1985 2000 2005 2010 2020];
tq = 1950:2100;
PFA = [11.197341 6.817398 6.056209 5.293600 4.327147 3.442431];
ypi = interp1(t,PFA,tq,'linear','extrap');
p = polyfit(tq, ypi, 2);
yp = polyval(p,tq);
subplot(2,1,1);
plot(tq,ypi);
title('polynomial fit');
fprintf('2 order polynomial = %e*t^2 + %e*t + %e ',p(1),p(2),p(3));

lPFA = log(ypi);
pe = polyfit(tq, lPFA, 1);
ype = polyval(pe,tq);
subplot(2,1,2);
plot(tq,ype);
title('exponential fit');
alpha = exp(pe(2))
beta = pe(1)
fprintf(' exponential = %e*e^(%e*t) ',alpha,beta);

Output: