Question 2.

A. population.m

function [pop] = population(t)
pop = 197273000./(1+exp(-0.0313.*(t-1913.25)));


B.

>> population(2050)

ans =

  1.9458e+008

C.

>> PopApprox = population(2010);
>> PopExact = 281421906;
>> PercentDifference = (PopExact - PopApprox) / ((PopExact + PopApprox)/2) * 100;
>> PercentDifference

PercentDifference =

   39.7182

D.

>> years = linspace(1790,2010,(2010-1790)*2);
>> popCurve = population(years);
>> plot(years,popCurve);

E.

>> title('George Hahn - G00207171');
>> xlabel('Year');
>> ylabel('Approximate United States Population');


Question 3.

A.

>> n = [5:5:100];
>> ApproxE = (1 + 1./(n)).^n;

B.

>> ApproxE(1,50/5) //Because we are counting by 5's

ans =

    2.6916

C.

>> PercentError = (ApproxE - exp(1))/exp(1)*100;

D.

>> plot(n,PercentError)
>> title('George Hahn - G00207171');