Name(s):                                                    .
Breakfast Line Rates
Tom Linton, Calculus 2, Central College, Spring 2002
Below is the graph of the rate r (in student arrivals per hour) at which students arrive for breakfast at CUIFS. The first students arrive at 8 AM and the line opens at 9 AM. Suppose that once the line is open, students can enter the cafeteria at the constant rate of 200 students per hour. Use the graph to find, or provide an estimate of:

 
  1. The rate at which students are arriving in the line at CUIFS at 10 AM.

    2.  

     
     
     

  2. The average value of r(t), from t = 8 AM to noon.



    3.  

  3. The length of the line at 9 AM, when CUIFS opens.



    4.  
     
     
     
     
     

  4. The length of the line at 10, 11, and noon.


    5.  










     
     

  5. The rate at which the line is growing at 10 AM.

    6.  

     
     
     
     
     
     
     

  6. The time at which the length of the line is a maximum.

    7.  

     
     
     
     







     

  7. The time it takes for a person who arrives at 9 AM to get in.

    8.  

     
     
     
     
     
     
     
     
     

  8. The time when there is no longer anyone in line.

    9.  

     
     
     
     
     
     
     
     
     

  9. Suppose you now had a formula, for the arrival rate r, in terms of t, say r(t). Explain how you would answer (write down formulas using r(t), integrals, certain times, etc.) each question above using r(t). For example, the answer to question 1 is just r(10 AM).