This one is for the birds

This weekend one of my students reported that he had gotten the following math challenge as part of the Thomas Jefferson High School of Science and Technology Student Information Sheet administration.  Applicants wrote answers to three SIS prompts and were given the following math question:

You have a population of 1000 penguins. 500 pairs produce one chick per pair per year. At the end of each year there is a loss of 20% of the total population. Figure out how many penguins there will be at the end of seven years. Develop a formula that solves the problem.