Question

A growing field of inquiry that both holds great promise and poses great risk for humans is nanotechnology, the construction of extremely small machines. Over the past couple of decades, the size that a working gear can be made has consistently gotten smaller. The table shows milestones along this path. Years from 1967 5 716 25 31 37 Minimum gear size [mm 0.8 0.4 0.2 0.09 0.007 2E-04 8E-06 (a) Graph the gear size (ordinate) versus the number of years from 1967 (abscissa) assum- ing the data are experimental. This plot should be a proper plot. (c) In a different experiment with different data, you determine the relationship to be MGS-2.5 e-0.5t. Create a proper plot of this expression using the fplot command, assuming the units for both the time and gear size are the same between the two data sets. (d) Use polyfit to determine an exponential relationship for the data set and plot the resulting relationship on a graph with the experimental data. This plot should be a proper plot using a logarithmic axis

Answer 1

year = [0 5 7 16 25 31 371: MGS = [0.8 0.4 0.2 0.09 0.007 2e-4 8e-61: plot (year, MGS, -*", 'LineWidth',1.2) grid on xlabel ("Number of Years from 1967") ylabel ("Minimum Gear Size [m]") title("Size Variation of Gear over Years") other Experiment plot using fplot figure (2) (t) 2.5 exp (-0.5*t) plot(E, [,37], 'LineWidth',1.2); grid on xlabel ("Number of Years from 1967") ylabel ("Minimum Gear Size [m]") title("Exponential Gear Size Variation over years") Fiting exponential figure (3) % Taking Log on both sides : % Log (MGS ) -Log (a) + b*t p -polyfit(year, log (MGS),1): exp fit MGSpolyval (p, year) plot (year,log (MGS),"*"); hold on plot (year,exp fit MGS, "LineWidth',1.2) legend (["Data Points", "Exponential Fit"], 'Location', "Best' xlabel ("Number offears from 1967") ylabel ("Log (MGS)") title("Exponential fit on semilog plot" grid on % Ploting Data Points % Ploting Fitted curve

Size Variation of Gear over Years 0.8 0.7 0.6 D 0.5 0.4 20.3 0.2 0.1 10 15 20 25 30 35 40 Number of Years from 1967	Exponential Gear Size Variation over years 2.5 N1.5 0.5 10 15 20 25 30 35 Number of Years from 1967
Exponential fit on semilog plot Data Points Exponential Fit -2 00 4 -4 -6 -8 -10 -12 20 Number of Years from 1967 10 15 25 30 35 40

Text :-

year = [0 5 7 16 25 31 37];
MGS = [0.8 0.4 0.2 0.09 0.007 2e-4 8e-6];

plot(year,MGS,'-*','LineWidth',1.2)
grid on
xlabel("Number of Years from 1967");
ylabel("Minimum Gear Size [mm]");
title("Size Variation of Gear over Years")

%Other Experiment plot using fplot
figure(2)
f = @(t) 2.5*exp(-0.5*t);
fplot(f,[0,37],'LineWidth',1.2);
grid on
xlabel("Number of Years from 1967");
ylabel("Minimum Gear Size [mm]");
title("Exponential Gear Size Variation over years")

% Fiting exponential
figure(3)
% MGS = a*e^(b)*t;
% Taking Log on both sides :
% Log(MGS) = Log(a) + b*t
p = polyfit(year,log(MGS),1);
exp_fit_MGS = polyval(p,year);
plot(year,log(MGS),"*");    % Ploting Data Points
hold on
plot(year,exp_fit_MGS,'LineWidth',1.2)      % Ploting Fitted curve
legend(["Data Points","Exponential Fit"],'Location','Best')
xlabel("Number ofYears from 1967");
ylabel("Log(MGS)");
title("Exponential fit on semilog plot")
grid on