Module 7: Rational Functions and Function Operations

 

In Try This 3 you will apply your understanding of multiplying and dividing functions to a problem that involves jet fuel.

 

In this graphic, numerous jets appear ready to land.

F1online/Thinkstock

Try This 3

 

Suppose that the volume of fuel a jet has used from the time it reaches its cruising altitude to time t is given by the function f(t) = 15 500t − 250t2, where f(t) is measured in litres and t is in hours. The distance the plane has travelled t hours after reaching its cruising altitude is d(t) = 900t, where d(t) is measured in kilometres.

  1. Determine a function, r(t), that gives the average rate of fuel use per kilometre for the cruising portion of the trip after t hours.
  2. If the cruising portion of the trip is expected to take 15 h, determine the domain and range of f(t), d(t), and r(t).
    1. Determine the average rate of fuel use per kilometre after 3 h and after 12 h.
    2. Explain the difference seen in question a.
  4. At what time is the average rate of fuel use 15.4 L/km?

course folder Save your responses in your course folder.

 

Share 2

 

With a partner or group, discuss the following questions based on the information in Try This 3.

  1. Why is r(t) meaningless when t = 0 in terms of the scenario?
  2. Why would question 4 of Try This 3 have been difficult if you didn’t use the quotient function r(t)?

course folder If required, save a record of your discussion in your course folder.



The range of f(t) and d(t) can be found by substituting 0 and 15 because both functions are always increasing during the flight. r(0) is indeterminate, so a graphical approach can be used to predict the range of r(t).
The average rate of fuel used can be measured in litres per kilometre.