1. Explain the difference between average and instantaneous rates of change. As part of your explanation, include the definitions and how they are interpreted on a graph. 2. A 2-L plastic pop bottle is filled with water. A hole is made in the base of the bottle. As the water drains out, the height of the water level in the bottle drops. The table show the height of there at 20 5 intervals. Time I (5} Height h {mm} 0 130 20 105 40 83 60 64 SD 43 100 34 120 22 140 13 160 6 180 2 200 0 Calculate the average rate of change between D s and 100 s and 100 s to 200 s. Does the bottle drain at a constant rate? Explain your reasoning. What does the negative rates of change indicate? Make as good an estimate as possible of the instantaneous rate of change of water height at t = 60 5. 0.0351) 3. As a snowball melts, its surface area and volume decrease. The surface area, S, in square centimeters is modelled by the equation 5 : 4an where r is the radius, in centimeters. The volume, V, in cubic centimeters, is modelled by the equation V = inri. a. Determine the average rate of change of the surface area and of the volume as the radius decreases from 26 cm to 18 cm. in. Estimate the instantaneous rate of change of the surface area and volume when the radius is 7 cm. c. From a) and b), how the average rate of change compare with the instantaneous rate of change. 4. A soccer ball is kicked into the air such that its height, h, in meters, after time, t, in seconds, can be modelled by the function hlt} = -4.9t2 + 18x + 1.5, 0 5 ts 3.755. a. Calculate the average speed ofthe ball using two times of your choosing. The times has to be between D and 3.755 s. b. Calculate the instantaneous speed of the soccer ball at time of your choosing. The times has to be between 0 and 3.755 s. Calculus and Vectors Lesson 1 5. Create a video (using your phone or a screen recording software such as screencastify or screencast-o-matic) answering the following question. In an object was thrown upward at 64 ft/s from a height of 20 feet, its height h after t seconds is given by hlt) = 20 + 54x 16x2. Calculate the a. average velocity between 1 and 2 seconds. b. instantaneous speed at 3 seconds