Modeling and Interpreting Real-World Periodic Functions

A Ferris wheel has a radius of 15 meters and completes one full rotation every 2 minutes. If a passenger starts at the lowest point, write a periodic function to model their height above the ground as a function of time. What is their height after 3 minutes?

• 0 meters

• 7.5 meters

• 15 meters

• 30 meters

The tides in a coastal area can be modeled by a sine function with a period of 12 hours. If the high tide occurs at 2 PM and the height of the tide is 3 meters at that time, write a function to represent the height of the tide over time. What will be the height of the tide at 8 PM?

• 4 meters

• 2 meters

• 3 meters

• 1 meter

A pendulum swings back and forth, completing one full cycle every 4 seconds. If the maximum displacement from the center is 10 cm, create a periodic function to model the position of the pendulum over time. What is the position of the pendulum at 6 seconds?

• 10 cm

• 0 cm

• -10 cm

• 5 cm

A sound wave can be modeled by the function y = 2sin(πt) where y is the amplitude in decibels and t is time in seconds. Determine the maximum and minimum sound levels produced by this wave.

• Maximum sound level: 2 decibels, Minimum sound level: -2 decibels

• Maximum sound level: 3 decibels, Minimum sound level: 0 decibels

• Maximum sound level: 1 decibel, Minimum sound level: -1 decibel

• Maximum sound level: 4 decibels, Minimum sound level: -3 decibels

A clock's minute hand moves in a circular motion, completing one full rotation every hour. If the length of the minute hand is 20 cm, write a function to model the height of the tip of the minute hand above the table as a function of time. What is the height after 15 minutes?

• 30 cm

• 20 cm

• 60 cm

• 40 cm

The temperature in a city varies throughout the day and can be modeled by the function T(t) = 10 + 5cos(π/12(t - 6)), where T is the temperature in degrees Celsius and t is the time in hours. What is the maximum temperature during the day?

• 5 degrees Celsius

• 20 degrees Celsius

• 15 degrees Celsius

• 10 degrees Celsius

A cyclist rides in a circular path with a radius of 50 meters, completing one lap every 3 minutes. Write a periodic function to model the cyclist's distance from a fixed point on the path over time. How far is the cyclist from the starting point after 5 minutes?

• 60 meters

• 40 meters

• 10 meters

• 25 meters

The brightness of a streetlight varies throughout the night, modeled by the function B(t) = 8 + 4sin(π/6(t - 12)), where B is the brightness in lumens and t is the time in hours after sunset. What is the brightness at 3 AM?

• 4 lumens

• 10 lumens

• 2 lumens

• 6 lumens

A swing moves back and forth, completing a full swing every 2 seconds. If the maximum height of the swing is 1.5 meters, create a function to model the height of the swing over time. What is the height of the swing at 1 second?

• 2 meters

• 0 meters

• 0.75 meters

• 1.5 meters

The population of a certain species of fish in a lake can be modeled by the function P(t) = 100 + 30sin(π/6t), where P is the population and t is the time in months. What is the population after 12 months?

• 110

• 90

• 130

• 100