Modeling with Periodic Functions Answers

Suppose that you want to model the height of a rider on a Ferris wheel as a function of time. The amplitude of the function you use as a model should be equal to which of the following?

Tides in a specific location can be approximated using the periodic function shown on the graph.What is the interpretation of the amplitude in this application?

The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation . What is the period of the function?

Throughout the day, the depth of water at the end of a dock varies with the tides. The function represents the height, in feet, of the water t hours after midnight.Which graph shows the height of the water at the dock at any time after midnight?

The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation . What is the maximum displacement of the tuning fork?

Which of the following situations can be modeled with a periodic function?

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. When the weight it released, it oscillates and returns to its original position at t = 3 seconds. Which of the following equations models the distance, d, of the weight from its equilibrium after t seconds?

Blood pressure can be modeled by a sinusoidal curve, where the maximum and minimum on the curve correlate to the person’s blood pressure reading. Henry’s blood pressure is modeled by the function , where t is time in seconds.Which graph accurately depicts this model?

The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation . How long does it take for the waterwheel to complete one turn?

The equation models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance.