#===========================================================
# Figure 10.7.R.
# R script to plot Hubbert's model of oil production.
#===========================================================
k=100      # Maximum amount of recoverable resource.
b=.5       # Resource depleted faster if b is larger.
m=1        # Initial amount produced is m.
t=(0:100)*20/100  # Range of values of time t from 0 to 20.
s=.01      # Small interval of time.
change.n=k/(1+((k-m)/m)*exp(-b*(t+s)))-k/(1+((k-m)/m)*exp(-b*t))
           # Amount of oil extracted between time t and time t+s.
rate.n=change.n/s  # Rate of oil production between time t and time t+s.
plot(t,rate.n,type="l",lty=1,xlab="time",ylab="rate of oil production")