Question

A passenger is riding a Ferris wheel. The graph shows the height, in feet, of the passenger as a function of time.



Short description, A graph.,Long description,
The graph shows Time in minutes on the x-axis and Height above the Ground in feet on the y-axis. A wave starts at (0, 5) and has a minimum value of 5 and a maximum value of 45. The wave completes 3 cycles every 2 minutes.


Question
Move values to the boxes to create a function, h of t, that models the height, in feet, of the passenger after t minutes on the Ferris wheel.

Response area with 3 blank spaces
h of t equals negative
Blank space 1 empty
cosine left-parenthesis
Blank space 2 empty
pi T right-parenthesis plus
Blank space 4 empty
Answer options with 6 options.

Answer 1

h(t) = -20 cos(3π t) + 25

(blank 1 = 20, blank 2 = 3, blank 4 = 25)

Reason: amplitude = (45−5)/2 = 20, midline = (45+5)/2 = 25, period = 2/3 min ⇒ coefficient B satisfies 2/B = 2/3 ⇒ B = 3.