In order to improve both the economy and quality of life, policies are designed to encourage growth and decrease traffic flow. In particular, the number of vehicles is encouraged to increase by a factor of 1.6 over each 10-year period, but the commuters from 10,000 vehicles are to choose to ride comfortable new trains instead of driving.
a. If there were 40,000 vehicles in 1970, how many would there be in 1980?
b. Find the discrete-time dynamical system describing this traffic.
c. Find the equilibrium.
d. Graph the updating function and cobweb starting from an initial number of 40,000.
e. In the long run, will there be more or less traffic with this policy than with the policy that led to the data in the previous problem? Why?