Many years ago, a large jetliner crashed into the ocean. No one could ever find the plane or any of its passengers or crew. The outside world did not know that there were many survivors. They made their way to two separate islands.
The islands, known as Uniformia and Ignoramia, were uninhabitated before the survivors arrived. They made pleasant lives for themselves. There is always plenty of food and water. The weather is always good. No one ever leaves, there are never any newcomers, and there will never be a rescue. By now, everyone is too old to reproduce. There are never any accidents, murders, or suicides.
People on both islands die only from natural causes, but in a very unnatural way. If anyone dies in a particular year, it happens at noon on September 1st. It is even possible to find out exactly when each person will die, but most would rather not know.
It is now the afternoon of September 1, 2012. One hundred people remain on Uniformia. They will die at a constant rate over the next ten years: ten in 2013, ten in 2014, and so on through 2022. The average life expectancy of the people on Uniformia is now 5.5 years. Their life expectancy will decline as each year passes.
There are also one hundred survivors on the island of Ignoramia. Their easy island life has never demanded abstract thinking, which is good since most Ignoramians hate mathematics. In particular, most believe that algebra is unnecessary.
Franz is the only Ignoramian who likes math. He calculates the average life expectancy of the people on his island. It is only 1.6 years. This is alarming news to the other Ignoramians.
Franz offers them a deal. If they put him in charge of the island, he promises that next year the average life expectancy will improve to 2 years. The year after that, it will be 3 years, and then 4, and then 5.
The Ignoramians do not understand how this is possible, but they trust Franz and agree to his deal.
As the years pass, the average life expectancy changes exactly as Franz promised:
|Date (September 1)||Average Life Expectancy (years)|
The Ignoramians are grateful to Franz. What did he do to improve their life expectancy?
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