Page 360 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 343

11(
026
7.32. N = 16,620e° ; N 0 = 16,620 7.33. (a) JV= 100e-°- '; (b) 4.05 yr
W5
7.34. N = N 0e-°- >;t 1/2 = 6.6hr

7.36. $15,219.62 7.37. $16,904.59
7.38. $14,288.26 7.39. 8.67 percent

7.40. 10.99 percent 7.41. 20.93 yr

7.42. 7.93 yr 7.43. 12.78 percent

7.44. 8.38 yr 7.45. r=-100e-° 029 <+100;
(a) 23.9 min; (b) 44° F

7.46. T = 80e-° 035( ; T 0 = 80° F 7.47. r=-100e-° 029 '+ 150; f 100 = 23.9min

7.48. (a) 138.6°F; (b) 3.12min 7.49. (a) 113.9°F; (b) 6.95 min

7.50. An additional 1.24 min 7.51. (a) v = 32t; (b) 16t 2
7.52. (a) 5.59 sec; (b) 5.59 sec 7.53. (a) 32J + 30; (b) 3.49 sec

7.54. (a) 32t+ 10; (b) 5 sec 7.55. 31.25 sec

7.56. 976.6 ft

4
2 3
7.58. (a) v = 48 - 48e- " ; 7.59. (a) v= 128- llSe"" ;
2 3
(b) x = 72e- " + 481-72 (b) 6.472 sec
7.60. 320 ft/sec 7.61. 0.392 m/sec with g = 9.8 m/sec 2

1(
7.62. (a) v = -320e-° + 320; 7.63. (a) v=4-4e8r
lt
(b) x = 3200e-°- + 320?-3200;
(c) 6.9 sec

2t
10
7.64. (a) v = 320 - 320e-" ; 7.65. (a) Q = -5e-°- + 5;
10
(b) x = 3200e-" + 320f - 3200
04
7.67. (a) g = 80e-° ';
at f = 10, 2 = 22.5 Ib (b) 17.3 min
(Note that a = 80(1/8) = 10 Ib.)

7.68. 56.3 Ib 7.69. 111.1 g
7.70. 80 g