While flying between San Francisco and Honolulu, a trainee actuary notices a new island 500 miles off the coast of California. He alerts the authorities and, soon later, the island is subject to a detailed study. Scientists discover that a new species of beetle inhabits the island and a sample of 50 beetles are returned to a research institute in San Diego. In the laboratory environment, the beetle population is observed to grow at a rate proportional to its population and such that, without any other influences, the population would quadruple every 5 weeks. On any given week, 20 insects are extracted from the population and dispatched around the world for further study, and 5 die of natural causes. Determine how long you might expect the beetle population to survive in San Diego.