Average versus Instantaneous Rate of Change Practice Questions 1. Determine if the statement below represent average, close to instant or instant rates. a) Some road tolls in the U.S. give speeding tickets based on the time it takes you to travel between exits. b) A police officer pulls you over for speeding since her radar gun displays 130 km/hr. c) Canada's population grew at a rate of 0.869% from 2006 to 2007. d) Roy Halliday's fast ball was measured to have a velocity of 152 km/h. e) Your parents kept a growth chart from the time you were 1 until you were 5 years old. They have calculated that your growth rate in that period was 9 cm/year. f) In 1996, Hurricane Bertha had wind gusts up to185 km/h. At some times during Hurricane Bertha the wind was gusting at 100 km/h. Water is being poured into a container. The rate in which the water level increases between 0 and 5 seconds of the pour is 7 mm/sec. h) A CO, probe measures the rate of increase of atmospheric COz. The probe reads an increase of 1.7 x 10"ppm/sec. 2. In general, does the speedometer of a car measure average or instant rate of change. Describe a scenario in which the average speed and instant speed would be the same. 3. Sketch the curve y = (1/2(x - 3))2+ 4 a) Calculate the average slope (secant) from 0 to 3 seconds Draw a tangent at x = 7. Calculate the slope at this point Describe what happens to the rate of change from 0 to 3 seconds Describe what happens to the rate of change from 0 to 6 seconds e) Describe when rate of change is zero 4. The diagram below describes the height of a ball thrown into the air according to the formula h(t) = - 3(t-2.5) + 25. Determine: Figure 1: Height vs. Time (2.5,25) a) the minimum height ball reaches b ) the initial height from which ball was thrown 30 c) describe interval when ball's height decreases 25 d) 20 the average rate at which the ball's height changes from; i) 0 to Is 15 Height (n ii) 0 to 4s 10 e) the instantaneous rate at which the ball's height changes at; i) 4s 2 3 6 7 ii) 2.5s Time ($)