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MHF 4UB Unit IV Workbook Lesson 16 Workbook Rates of Change Do not use calculus for any solutions in this lesson. Support Questions 16A 1. A ball is tossed into the air. Its height, h, in metres, at time t, in seconds, can be modeled by h() =20r -4.9. Determine the average rate of change between 2 s and 3 s. 2. City engineers estimate that the accumulation of solid waste, f, in tonnes, at the city landfill can be modeled by f() =92(r*+12/ +80) where t is the number of years since 1990. What is the average rate of increase in waste from 1995 to 2000?Support Questions 16B 3. A pebble falls from the top of a cliff that is 180 m high. The pebble's height above the ground is modeled by h() = -5/ -5/+180, where h is the height in metres at t seconds since the pebble started to fall. Find the instantaneous rate of change in height at 3 s. 4. A population of algae in a swimming pool starts at 2500. After 15 minutes, the population is 5000. This population can be modeled by the equation P() = 2500(16)' where P is the population after t hours. a) Find the algae population after ten minutes. b) Estimate the instantaneous rate of change of the algae population at one hour.5. The average speed of a certain particle in metres per second is given by the 217 + 8+5 equation S(() = Find: 1+3 a) the average rate of change as time changes from 0.5 s to 3.5 s. b) the instantaneous rate of change at 3.5 s.6. After you eat something that contains sugar, the pH or acid level in your -20m mouth changes. This can be modeled by the function L(m) = + 6.5. m+36 where L is the pH level and m is the number of minutes that have elapsed since eating. Find; a) the average rate of change from 1.5 minutes to 3 minutes b) the instantaneous rate of change at 3 minutesMHF 4UB Unit IV Workbook 5 7. The vertical position of a person on a Ferris wheel can be modeled by the equation h() =-10cos 15 + 1 1. Height h is in feet while t is in seconds. (Answer accuracy: 2 decimal places) a) Sketch the graph of this function for the interval [15,30]. b) Find the average rate of change as t goes from 24 s t 24.5 s. c) Find the instantaneous rate of change at t = 24 s