6-6

“A” is for amplitude. This is ½ the distance from the highest and lowest value. So……. Highest Value – Lowest Value 2

“h” is the Vertical Shift. The midline is ½ the sum of the highest and lowest values. So…….Highest Value + Lowest Value 2

“k” helps find the period. Look for how long it takes the data to repeat. “c” helps find the phase shift. Plug in an actual value from the data for x and for y then solve for “c”

MonthJanFebMarAprMayJuneJulyAugSeptOctNovDec t Hrs Daylight Find the Amplitude and the Vertical Shift. A = 1.61 h = Next determine the “k” value by finding the period. k = π 6 Finally, determine the “c” value by plugging in an x and y value. c = y = 1.61 sin (π/6 – 1.66)

Suppose the lungs have a minimum amount of air at t = 0, where t is the time in seconds. Write a function that models the amount of air in the lungs. A= 0.37 h = 0.45 k = π/2 c can not be found because there are no data points y = cos (π/2 t) +0.45

Suppose the diameter of the Ferris Wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet about the ground. Write an equation to model your ride on the Ferris wheel.

L = sin (π/5 t) H = cos (π/5 t) A. Determine the maximum and minimum number of Lynx. B. Determine the maximum and minimum number of Hares. C.How many years will it take for the first minimum of Hares to occur? D.What will the populations of Lynx and Hares be after 15 years have gone by?

Write a model for the height, h, of the rope as a function of time, t, given that the rope is at its lowest point when t = 0. pg 508 pic

The highest point of the handle at the edge of the flywheel is 9 feet above the ground, and the lowest point is 4 feet. Write a model for the height h (in feet) as a function of time t (in seconds) given that the handle is at its lowest point when t = 0.

The reflector makes one revolution per second. Write a model for the height (in inches) of a reflector as a function of time (in seconds) given that the reflector is at equilibrium point when t = 0.

pg 531 table

 pg graphs.