Math 154 Name:
Quiz # 8
1. A ferris wheel is 40 meters in diameter and is boarded from a platform that is 5 meters above the ground.
The wheel completes one rotation every 8 minutes. Let f(t) be the height above the ground (in meters) of a
rider on this ferris wheel tminutes after boarding.
(a) (5 pts.) Sketch a graph of f.
0
10
20
30
40
50
2 4 68 10 12 14 16
y=f(t)
Note the highest height a passenger on this ferris wheel attains is 45 meters.
(b) (10 pts.) Find a formula for the function f. Using complete sentences, explain how you found your
formula.
Different solutions are possible. Examining f, we note the following properties:
•The period is 8.
•The midline is 25.
•The amplitude is 20.
If we start with the sine function, we note that we have to stretch the sine function
vertically by a factor of 20 in order to get the proper amplitude. This will require
an outside multiplication by 20. The period of the sine function is 2π. This will
need to be changed by a factor of 8
2π=4
π. Thus, we need a horizontal stretch by
a factor of 4/π. This will require an inside multiplication by π/4. Finally, in order
to change the midline to 25, we will have to have an outside addition of 25. So, we
might hypothesize that fshould have the following formula: f(t) = 20 sin π
4t+25.
This is however incorrect.
