At the conclusion of the Super Bowl, the number of fans remaining in the stadium decreases at a rate proportional to the number of fans in the stadium. Assume that there are 100,000 fans in the stadium at the end of the Super Bowl and ten minutes later there are 80,000 fans in the stadium.
(a) Thirty minutes after the Super Bowl will there be more or less than 40,000 fans? How do you know this without doing any calculations?
(b) What is the half-life (see the previous problem) for the fan population in the stadium?
(c) When will there be only 15,000 fans left in the stadium?
(d) Explain why the exponential decay model for the population of fans in the stadium is not realistic from a qualitative perspective.
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