Unit 7 Test James Reede, Ed. S. AP Calculus AB Name: Multiple Choice 1. Solve the equation. f'(x) = 6f(x) and f(2) = 9 A. f(x) = 6ex+2 B. f(x) = 9e2x+6 C. f(x) = 9ear-12 D. f (x) = ear+9 [2 Marks] 2. Shown at right is the slope field for which differential equation? A. B. dy C. dy dx D. [2 Marks] 3 The rate of growth of a bacteria population is proportional to the number of bacteria present. The initial population quadrupled during the first 2 days. By what factor will the population have increased during the first 3 days? A. 4 B. 5 C. 6 D. 8 [2 Marks]nit 7 Test James Reede, Ed. S. Name: AP Calculus AB 4. The amount of pain reliever in Tony's bloodstream decreases at a rate that proportional at any time, to the amount of pain medication in the bloodstream at that time. Tony takes 180 milligrams of the pain reliever initially. The amount of medication is halved every 3 hours. How many milligrams of the medication are in Tony's bloodstream after 8 hours? A. 28 mg B. 68 mg C. 116 mg D. 143 mg [2 Marks] Which of the following differential equations has x3 - 4y2 = 8 as a solution? A. dy = 4xy B. ay = - C. y dx D. Ay [2 Marks] 6. Contaminated water is being pumped continuously into a tank at a rate that is inversely proportional to the amount of water in the tank: that is, of =} Ly = 5, where y is the number of gallons of water in the tank after t minutes (t 2 0). Initially, there were 5 gallons of water in the tank, and after 3 minutes there were 7 gallons. How many gallons of water were in the tank at t = 18 minutes? A. 17 B. V97 C. V61 D. 13 [2 Marks]James Reede, Ed. S. AP Calculus AB Name: Questions 7 and 8 refer to the following information: 7. Consider the differential equation = >, for which the solution is y = f(x). Let f(0) = 1 Which of the following statements about the graph of f(x) are true? I. f (x) has a vertical tangent when y = 0 II. f (x) has a horizontal tangent when x = 0 III. The slope of f(x) at the point (0.1) is 1. A. I only B. II only C. I and II only D. I, II, and III [2 Marks] 8 The particular solution is A. f(x) = V2 cosx +3 B. f(x) =V3-2 cosx C. f(x) = - ecos.x D. f(x) = 3e-2cosx [2 Marks]prede, Ed. S. culus AB Name: The radiation R(t) in a substance decreases at a rate that is proportional to the amount present; that is, at = kR, where k is the constant of proportionality and t is the time measured in years. The initial amount of radiation is 7600 rads. After three years, the radiation has declined to 500 rads. (Note: One rad = 0.01- is a unit used to measure absorbed radiation doses). A) Express R as a function of time. B) When will the radiation drop below 20 rads? C) Find the half-life of this substance.7 Test mes Reede, Ed. S. up Calculus AB Name: Free Response A) Given 41 = -4 find the general solution algebraically. B) Then, sketch a solution of the differential equation on the slope field that passes through (2, 0)