Determine if the given function y = f(x) is a solution of the accompanying differential equation. my+y=e2x 1) y =9e- * + 2x A) Yes B) No Solve the differential equation. 2) x2 01 - 2y dx 2) _ A)y = - -+C By = Ce2/x Q y = Ce- 2/x Djy = Ce- 2x dy =7x6e-y 3) dx 3) A)y=x + C B)y = Cln (x7) gy = In (x7+q) D) y = In (7x7 + c) dy = 6x56052 y 4) dx A) y = tan (x6 + () Bjy =x6+ C C y = tan-1 (x6 + 0) Djy = tan-1 (x5 + () Solve the initial value problem. dx 5) 2-4 - 4xy = 8x; y(0) =22 5) A) y=-1 + 230*2 B)y = 2+22ex2 Oy=-2+ 24e-x2 D) y = -2 + 24ex2 Solve the problem. 6) A bacterial culture has an initial population of 10,000. If its population declines to 4000 in 6 hours, 6) when will its population be 2947? Assume that the population decreases according to the exponential model. A) after 9 hours B) after 5 hours C) after 8 hours D) after 7 hours Use Newton's Law of Cooling to solve the problem. 7) A dish of lasagna baked at 375-F is taken out of the oven into a kitchen that is 72"F. After 7 7) minutes, the temperature of the lasagna is 309.2"F. What will its temperature be 17 minutes after it was taken out of the oven? Round your answer to the nearest degree. A) 239-F. B) 227-F. C) 246-F. D) 234-F. Find the area enclosed by the given curves. 8) y = 2x - x-, y = 2x - 4 8) A) -= B) 3Find the area of the shaded region. 9) V = 2x-+x-6 V=x2-4 5+ 3- 24 -3 -2 19 IE A)- B) 1 DJ Calculate the area of the region bounded by the graphs of the given equations. 10) x =2y2 - 2, x =y2 +7 10) 110 A) 36 BJ 3 () 27 D) 12