Question 1(Multiple Choice Worth 5 points) [[3 (07.01) The temperature of a pot of coffee varies according to Newton's Law of Cooling: % = k(T A), where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the water cools from 90C to 85C in 1 minute at a room temperature of 30C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes. O72 042 068 081 Question 2(Multiple Choice Worth 5 points) (07.01) The rate of decay in the mass, M, of a radioactive substance is given by the differential equation any time t. O M = 200ln(kt) O M = 2e"kt O M = 200 ekt O M = 200 ekt dM [S kM, where k is a positive constant. If the initial mass was 2009, then nd the expression for the mass, M, at Question 3(Multiple Choice Worth 5 points) (07.02) The differential equation Y _ y-2 dx y + 1 I. produces a slope field with horizontal tangents at y = 2 Il. produces a slope field with vertical tangents at y = -1 Ill. produces a slope field with columns of parallel segments Ol only O II only Ol and II O Ill only8 Question 4(Multiple Choice Worth 5 points) I (07.03) 3 Estimate the value of Ix'dx by using the Trapezoidal Rule with n = 4. I 019 022 Question 5(Multiple Choice Worth 5 points) (07.02) Which of the following differential equations is consistent with the following slope eld? Ti Question 6(Multiple Choice Worth 5 points) (07.01) The slope of the tangent to a curve at any point (x, y) on the curve is 2. Find the equation of the curve if the point (3, -4) is on the curve. Ox+y=4 O x2 + y2 = 5 O x2 + y = 25 Oxzy2=-7 |||| . 0 with f '(x) 0 for all x in the interval [0, 2] with f(0) = 1 and f(2) = 0.2, the left, right, trapezoidal, and midpoint rule approximations were used to estimate l[i(x)dx . The estimates were 0.7811, 0.8675, 0.8650, 0.8632 and 09540, and the same number of subintervals were used in each case. Match the rule to its estimate. Match Term Definition left endpoint A) 0.8650 right endpoint B) 0.7811 midpoint C) 0.9540 trapezoidal D) 0.8632 actual area E) 0.8675 Question 8(Multiple Choice Worth 5 points) (07.01) Find the particular solution to y ' = 3sin(x) given the general solution is y = C - 3cos(x) and the initial condition y(TT) = 1. 0 4 - 3cos(X) O-2 - 3cos(x) O 2 - 3cos(x) O-4 - 3cos(x)Question 9(Multiple Choice Worth 5 points) (07.03) 2 The tab e below gives selected values for the function f(x). With 5 rectangles, using the midpoint of each rectangle to evaluate the height of each rectangle, estimate the value of Jf(x)dx . 1 x 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 f(x) 1 0.909 0.833 0.769 0.714 0.667 0.625 0.588 0.556 0.526 0.500 0 0.7456 0 0.6456 00.6919 0 0.6932 [2 Question 10(Multiple Choice Worth 5 points) I (07.02) The general solution of the differential equation x dx - y dy = 0 is a family of curves. These curves are all 0 hyperbolas O circles O parabolas O ellipses