### Before First Class

TBA

### Before Second Class

**Q107.** Our neighborhood association has a ten member board. Each year it plans to add four members. Write the difference equations that describe the size of the board (S) each year.

**Q108.** You are a small non-profit. Your sole funder says that each year it will double what you have as your balance at the end of the year. Each year you project spending 20,000 for programs. Ignore interest. Write difference equations describing your balance (B).

What special situations can you imagine we might get into? What, for example, happens if B_{0}=$32,000? What happens if it is 50,000? 40,000?

**Q109.** Each year the feral cat population grows by 3%. Let C_{n} be the number of cats n years from now. Assume there are presently 350. Write a difference equation that describes the cat population from year to year.

**Q110.** Each year the feral cat population grows by 3%. Let C_{n} be the number of cats n years from now. Assume there are presently 350. Suppose that each year we catch and euthanize or place in homes 20 cats. Write the equations for this situation.

**Q111.** Let's say we have a 2 year graduate program. The first year class is growing at a rapid rate 5% per year. Between the first and second years, 25% of the students change their minds or get jobs and leave the program. Among the second years, 10% leave before graduation. The program currently has 20 first year and 12 second year. Write difference equations to describe population in future years.

### Before Lab

**Q136.** Write out the difference equation that represents the following scenario and the first five terms of the corresponding sequence given the stated starting value.

- Membership in a club goes up by 4 people each year. At year one it has 21 members.
- A community's population increases by 4% each year. At year one it is 350.
- A swimming pool, currently containing 100,000 gallons of water, is leaking at the rate of 2% per day but is being filled at the rate of 1,000 gallons per day.
- A retirement account which stands at $120,000 earns 3% interest annually. The owner needs to withdraw $1500 per month to pay for eldercare.

For each of these, graph P_{n} vs. time.

For each of these, graph P_{n+1} vs. P_{n}