The global production of platinum in $2011$ stands at about $178$ metric tons per year, most from South Africa. The catalytic converter of a car requires about $1$ gram of precious metal catalyst, most commonly, platinum. Car manufacture in $2011$ was approximately $52$ million vehicles. If all have platinum catalysts, what fraction of the world production is absorbed by the auto industry? If the production rate of cars is growing at $4\%$ per year and that of platinum is constant, how long will it be before the demand exceeds the total global supply?