Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0204
Writing linear equations that model real-world problems is a useful tool of algebra.
| Ex. #1 | Suppose an airplane descends at a rate of 700 ft/min from an elevation of 20,000 ft. Write an equation to model the plane's elevation as a function of the time it has been descending. |
| Relate |
plane's elevation = rate · time + starting elevation |
| Define | Let d = the plane's elevation |
| Let t = time (in minutes) since the airplane started to descend | |
| Write | d = – 700· t + 20000 |
| What will the plane's elevation be after 15 minutes of descent time? | |
| Solve | d =
– 700· t + 20000 d = – 700(15) + 20000 d = – 10500 + 20000 d = 9500 ft. |
| Ex. #2 | Use the equation from Example #1 to find what the plane's elevation will be after 15 minutes of descent time. |
| Model | d = – 700· t + 20000 |
| Solve | d =
– 700· t + 20000 d = – 700(15) + 20000 d = – 10500 + 20000 d = 9500 ft. |
| Ex. #3 | At this rate, how long will it take before the airplane can land? |
| Model | d = – 700· t + 20000 |
| Know | The airplane will land when the distance is zero |
| Solve | d =
– 700· t + 20000 0 = – 700t + 20000 – 20000 = – 700t t = 28.57 min. |
| The airplane will be able to land about 29 minutes after it begins its descent. |