Q Q 1. (07.01 MC) A heat source is applied to a metal surface, causing the temperature of the metal to increase with respect to time at a rate that is proportional to the sum of the metal's instantaneous temperature, 7, and the metal's original temperature, To. Select the differential equation that represents the relationship. (10 points) di = CT +T O dT = c(T + To) dt O T = t (T + To) O T = 1 ( To + T) Q Q 2. (07.01 MC) Determine the value of k that will make y = 2cos(2x) a solution to ky + y " = y. (10 points) O k =5 OK=0 OK = - 3 OK = - 6 Q Q 3. (07.01 MC) by =2+3y. Select the general solution to dx (10 points) 1. - In/ 2 + 3y)= In/x|+C 11. In 2 + 3y|-C= In|x| OI O II Both Neither[:J [3 440102 MC] A slope eld is shown for which ofthe following differential equations? (\"I 0 points) [:J I 5.(n?.nzmc] =2x+y 3 dx Based on the graph ofthe general solution to the differential equation ' which of the following statements is true? [10 points] 0 "he slopes along the yaxis are horizontal. "he slopes along the xaxis are horizontal. 0 "he slopes are all positive in Quadrant 'I. 0 "he slopes are all positive in Quadrant 4. 6. (07.02 MC) dy _X The general solution of the differential equation X } where y = 0, is a family of which of the following? (10 points) O Parallel lines Hyperbolas Parabolas Lines passing through the origin Q Q 7. (07.04 MC) dy = xy +3x? What is the general solution to the differential equation dx (10 points) O dy y+3 dx 1 - X O y=e2 -3+C O y=e 3x+C O x2 y=e2 -3 8. (07.04 MC) dy 2xy Which of the following is the solution to the differential equation dx x2 +1 with the initial condition y(1) = 2? (10 points) Oy= x2 +2 O y = Inlx 2 + 21 O y= In(x2 + 11 + In(2) Oy=x2 +1Q 9. (07.04 MC) dy = -4xy's, with the initial condition f(-1) = -1. Which of the following gives an expression for f(x) and the domain for which the solution is valid? (10 poin Let y = f(x) be the particular solution to the differential equation dx O f ( x ) = 1 - ( 3 ) 14x2 -3 for and O f ( x ) = 1 V/4x2 -3 for (- co -V3) and ( V3, 00) O f ( x ) = - 1 ( 3 ) V4x2 -3 for and Of ( x ) = 1 V/4x2 -3 for (- 00 -V3) and ( V/3, 00) 10. (07.05 MC) The rate at which a particular medication leaves an individual's bloodstream is proportional to the amount of this medication that is in the bloodstream. An individual takes 200 mg of the drug initially. The amount of medication is halved every 12 hours. Approximately how many mg of the medication remain in the individual's bloodstream after 7 hours? (10 points) 127 mg O 133 mg O 150 mg 174 mg