(key Q16)

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MHF 4UB Unit IV Workbook 6 KEY QUESTIONS Lesson 16 1. Knowledge/Understanding/Application [8 marks] The points P(2,5) and Q(3, 12) lie on the parabola y= x* + 2x - 3. a) Find the slope of the secant PQ. b) Find the slope of the tangent (instantaneous rate of change) to the parabola at P. c) Find the equation of the tangent at P. d) Graph the parabola, the secant, and the tangent.2. Communication [2 marks] The annual amount of waste taken to a landfill site can be modeled by the function w(/) =1 10(1 +15t + 40), where w is measured in tonnes and t is the number of years since 1990. Explain the meaning of each expression in terms of the landfill site. a) W(10) - w(5) 10-5 b) W( 4.001) - w(4) 0.001 MHF 4UB Unit IV Workbook 3. Application [8 marks] The ratio of surface area to volume of a cylinder of radius 7 cm is given by the function f (h) = 14ah+98x . where h represents the height of the cylinder in cm. Find: a) a simpler algebraic form for this function b) the ratio of surface area to volume at a height of 4 cm c) the average rate of change as height changes from 4 cm to 9 cm d) the instantaneous rate of change at 9 cm4. Thinking/Inquiry/Problem Solving [6 marks] Fluorine-20 is a radioactive substance that decays over time. At time 0, the mass of a sample of the substance is 20 g. The mass decreases to 10 g after 11 s, to 5 g after 22 s, and to 2.5 g after 33 s. Compare the average rate of change over the 33-s interval with the average rate of change over consecutive 11-s intervals