Questions to ponder: 1. How are you going to represent the problem through a function? 2. What is/are the given in the problem? What are you going to solve? 3. How can you describe the relationship between the rate r and the time t in the problem? Which do you think is the variable that depends on the value of another variable? 4. What can you say about the graph? Can the values in t increase infinitely? 5. What do you think would be the value of r when t is equal to zero?

5. Let's apply our knowledge of functions and their inverses to a real world problem: To make a long-distance call, your phone company charges $1.50 to make the connection, and an additional $0.10 for every minute that you are on the line once connected. a. Write an equation for the price of a long-distance call, p, in terms of the length of the call in minutes, m: b. When you get the phone bill, you see that your sister made a long-distance call that cost $2.75. How long was she on the phone? Think about how you solved part (b). Write an equation to determine m in terms of p. (That is, how do you calculate the length of a call based on its price?) C.

2. A flu patient is prescribed a course of an antivirus drug. The number of mg of the drug in the bloodstream t hours after the first dose is taken is given by the function A(t) = 400te-³t. a. Sketch the graph of the function in an appropriate window, labeling axes and scale. I b. On what interval(s) is the amount of drug in the bloodstream increasing? Decreasing? c. When is the amount of the drug at a maximum? Label the corresponding point on the graph.

10. A thermometer reading 18° F is brought into a room the temperature of which is 70° F. One minute later, the thermometer reading is 31° F. Determine the temperature reading as a function of time, and in particular find the temperature reading 5 minutes after the thermometer is first brought into the room.