A country decides to subsidise the purchase of electric vehicles, causing more people to buy them.
Initially, the country used an equivalent of 56 million tonnes of oil for transport.
Since the government subsidy, the transport sector in each subsequent year has required 80% of the amount of oil that the previous year required.
a) Write a recurrence relation to model the amount of oil used, in million tonnes, in each subsequent year.
b) Find the amount of oil needed for the transport sector after the fifth year.
c) Find the total amount of oil used until the transport sector requires no more oil.
d) State one limitation with the model.