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7.1. INTRODUCTION TO PERIODIC FUNCTIONS. Ferris Wheel Height As a Function of Time. The London Eye Ferris Wheel measures 450 feet in diameter and turns continuously, completing a single rotation once every 30 minutes.

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7.1

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  1. 7.1 INTRODUCTION TO PERIODIC FUNCTIONS Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally

  2. Ferris Wheel Height As a Function of Time The London Eye Ferris Wheel measures 450 feet in diameter and turns continuously, completing a single rotation once every 30 minutes. Since the speed of the rotation is constant, you are at the top 15 minutes after boarding and one-quarter of the way up at 7.5 minutes and 22.5 minutes after boarding. Then you are back at the bottom after 30 minutes and the process continues. Values of f(t), your height above the ground t minutes after boarding the wheel Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally

  3. Graphing the Ferris Wheel Function Values of f(t), your height above the ground t minutes after boarding the wheel Notice that the values of f(t) in the table begin repeating after 30 minutes. This is because the second turn is just like the first turn, except that it happens 30 minutes later. If you ride the wheel for more full turns, the values of f(t) continue to repeat at 30-minute intervals.We plot this data and fill in the blank spaces. y (feet) t (minutes) Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally

  4. Periodic Functions: Period, Midline, and Amplitude The Ferris Wheel function, f, is said to be periodic, because its values repeat on a regular interval or period. The vertical distance shown between the first peak and the midline is called the amplitude. Period: One rotation takes 30 minutes Midline: Wheel’s hub is 225 ft above ground y (feet) Amplitude: Radius of wheel is 225 ft y = 225 t (minutes) The graph of y = f(t) showing the amplitude, period, and midline Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally

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