MCV4U Culminating I 1. Determine an equation of the line tangent to the curve y = ~5x -4 at the point with x-coordinate 4. [6] 2. Use the limit of a slope definition to determine the instantaneous rate of change of [6] Ax) = 3x at the point (3, 27). 3. A manufacturer of tennis balls determines that the profit from the sale of x cans of tennis balls per [4] week measured in hundreds is given by the function P(x) = 180x - 2x , where P is measured in dollars. Determine the rate of cans of tennis balls being sold for x = 3. 4. A city bus system carries 4000 passengers a day throughout a large city. The cost to ride the bus is [7] $1.50 per person. The owner realizes that 100 fewer people would ride the bus for each $0.25 increase in fare, and 100 more people would ride for each $0.25 decrease in fare. If the capacity of the bus system is 5000 passengers, what should the bus system charge to produce the largest possible revenue? 5. Differentiate the function A(x) = ~ 3cosx-* . [3] 6. A radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A() = 100-005t a. Determine the function, A , which represents the rate of decay of the substance. b. What is the half-life for this substance? [4] c. What is the rate of decay when half the substance has decayed