Write out clear and complete solutions to each of the following problems. Use graph paper and choose an appropriate scale so that the shape of your graph is clear.

1. Marissa is watching a honeybee return from her flower garden to a beehive in a branch of a nearby tree. She notices that the bee's path resembles part of a trigonometric function (see below). Suppose that the flower is 2 ft above the ground, the beehive is 8 ft above the ground, and the horizontal distance from the flower to the beehive is 20 ft. Model this path with a sine or cosine function. Clearly indicate the following: a. The maximum and minimum b. The midline c. The period and rate constant d. Write a formula for the function e. Clearly label all parts f. Sketch the graph You can check your work by graphing your function on a graphing calculator or a utility like desmos.com.2. The price of fresh, organic blueberries varies over the course of the year. In early July, when blueberries are abundant, a quart of organic blueberries may cost only $4.00. However, in January, a quart of organic blueberries may cost as much as $9.00. Model the price of blueberries using a sine or cosine function. Let x represent the number of months since the beginning of the year (so x = 0 means the beginning of January, and x = 6 means the beginning of July). Clearly indicate the following: a. The maximum and minimum b. The midline @ Copyright 2017 Michigan Virtual Revised10/9/2017 Page 1 . The period and rate constant d. Write a formula for the function Clearly label all parts f. Sketch the graph desmos.com. You can check your work by graphing your function on a graphing calculator or a utility like 3. Using the graph shown below, identify the maximum and minimum values, the midline, the amplitude, the period, and the rate constant. Then use that information to find a formula for the function. 45 (7.5, 40) -35 25 20 -15 2 3 5 11/ 12 13 14 (4.5. -10) --15