A series of locks manages the water height along a water source used to produce energy. As the locks are opened and closed, the water height between two consecutive locks fluctuates. The height of the water at point B located between two locks is observed. Water height measurements are made every 10 minutes beginning at 8:00 a.m. It is determined that the height of the water at B can be modeled by the function f(x) = -13 cos water is measured in feet and x is measured in minutes. What is the maximum and minimum water height at B, and when do these heights first occur? Drag a value or time into each box to correctly complete the statements. The first minimum water height of occurs at a.m. feet occurs at - 5+24, where the height of a.m. The first maximum water height of feet

The population of arctic foxes in Yukon can be modelled by the following equation: P = 400 cos(30t - 180) + 1100 Where 't' represents the number of years since 1992. a. b. C. d. c. What was the population of arctic foxes in Yukon in 1992? What are the maximum and minimum number of arctic foxes? Sketch a graph that represents how the population of artic foxes changes over time (since 1992). What will be the population of arctic foxes in 2030? When was the first time the population of arctic foxes reached 1300 (since 1992)?

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)

When drugs are administered into the bloodstream, the amount of the drug present decreases continuously at a constant rate. The amount of a certain drug, Xanaz, in the bloodstream is modeled by the function, where is the initial dosage, and t is the time (in hours) after the initial dose was given. The following chart shows the relationship between the original dose and how much is sti in the system after so much time. Xanax (3mg) amount still in system after X hours 2.5 1.5 0.5 2 10 12 14 16 18 20 22 24 Number of hours after dose was taken After how many hours will there be approximately 1/2 of the original dose in the body? 3. 2. 1. Amount still in the system in mg's