Question

A few years ago, you began an informal book club with your friends. Gradually, your ability to pick great books and facilitate amazing literary discussions has turned your small club into a city-wide phenomenon. With a significant waiting list to join your various clubs, you control the input vigorously. While most people who get into your club remain in the club, you lose 20% of members annually, and therefore allow 100 new members at the end of each year.

a. What is the long-term equilibrium of club membership? Is this a stable or unstable equilibrium, and how do you know?

b. Assume for this part only that rather than lose 20% and add 100 new members annually, you add 20% and lose 100 members annually. What is the long-term equilibrium now? Is it stable or unstable, and how do you know?

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Difference Equations Problems

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