A credit card has a nominal annual interest rate of 18%, and interest is compounded monthly. The cardholder uses the card to make a \$30 purchase.

Which expression represents the balance on the card after 5 years, in dollars, assuming no further charges or payments are made?

The expression \(1,\!500\cdot\left(1.085\right)^3\) represents an account balance in dollars after three years with an initial deposit of \$1,500. The account pays 8.5% interest, compounded annually for three years.

1. Explain how the expression would change if the bank had compounded the interest quarterly for the three years.
2. Write a new expression to represent the account balance, in dollars, if interest is compounded quarterly.

The function, \(f\), defined by \(f(t) = 1,\!000 \boldcdot \left(1.07\right)^t\), represents the amount of money in a bank account \(t\) years after it was opened. 

1. How much money was in the account when it was opened?
2. Sketch a graph of \(f\).
3. When does the account value reach \$2,000? 

A party will have pentagonal tables placed together. The number of people, \(P\), who can sit at the tables is a function of the number of tables, \(n\).

1. Explain why the equation \(P = 3n + 2\) defines this function.
2. How many tables are needed if 47 people come to the party?
3. How many tables are needed if 99 people come to the party?
4. Write the inverse of this function, and explain what the inverse function tells us.