︠bbc0d199-8c1e-4a04-b2c1-01d6ae5c3b23s︠
%default_mode r

︠46a8ffd8-b04c-418a-8dfd-8d4271e39b77s︠

#project 7 calculations
#exponential growth model
p_expon=33759742*(1.0080)^(c(0,5,10,15,20,25,30,35,40))


#affine model p(n)=1.0024*p(n-1)+189055

#define parameter values:
par1<-1.0024
par2<-189055
#number of time steps to be computed:
nmax=40
#create a vector to store the results for each time step:
p_sequence=c(0:nmax)
#choose an initial value and put it in the element of the vector:
p=33759742
#use a loop to compute the values:
for(i in 1:(nmax+1))
{p_sequence[i]=p;
pnext=par1*p+par2;
p<-pnext;
}
p_aff=p_sequence[c(0,5,10,15,20,25,30,35,40)+1]
p_meas=c(33759742,35099836,36387359,37558781,38564870,39395855,40070226,40635090,41135648)
p_all=cbind(p_expon,p_aff,p_meas)
timeseq=c(0,5,10,15,20,25,30,35,40)
matplot(timeseq,p_all,pch=20,type="b",xlab="n",ylab="population size")
#percentage difference affine = census after 10 years:
100*(p_aff[3]-p_meas[3])/p_meas[3]
#after 40 years:
100*(p_aff[9]-p_meas[9])/p_meas[9]

#modified model
#define parameter values:
par1<-1.0012
par2<-139600
#number of time steps to be computed:
nmax=40
#create a vector to store the results for each time step:
p_sequence=c(0:nmax)
#choose an initial value and put it in the element of the vector:
p=33759742
#use a loop to compute the values:
for(i in 1:(nmax+1))
{p_sequence[i]=p;
pnext=par1*p+par2;
p<-pnext;
}
p_sequence[41]-p_meas[9]

x<-c(1:100)
y<-log(x)
plot(x,y) #provides a plot with open circles

plot(x,y,pch=".") #gives a plot with points

plot(x,y,pch=20) #gives a plot with bullet points

︠01786e8e-7079-45d3-a6e3-86c718356954s︠
plot(x,y,type="l") #gives a line plot

plot(x,y,pch=20,col="red") #gives a plot with red bullet points

︠f7e9ee75-c366-4145-948d-d60cda28740c︠