Answers to even-numbered HW - Test 3

Answers to even-numbered HW - Test 3 - P ( t ) = P (0) e kt...

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Answers to Even-Numbered Homework Problems HW #14 - 20 HW 14 p. 187 4. e x ± 1 + 2 x 2 x ² 6. xe x (1 + x ) 2 8. 8 - 2 t 2 (4 + t 2 ) 2 10. 3 u 2 + 2 u + 2 u - 2 14. - 2 x 3 - 3 x 2 - 3 ( x 3 + x - 2) 2 22. 2 3 t - 1 / 3 + 1 2 t - 5 / 6 HW 15 p. 195 2. 2 x cos x + sin x 2 x 8. e u (cos u - sin u + c (1 + u )) 10. 1 x + cos x 22. y = x + 1 p. 203 2. y = f g ( x ) with f ( x ) = x 1 / 2 , g ( x ) = 4 + 3 x . dy/dx = 3 2 4 + 3 x 4. cos x · sec 2 (sin x ) 6. e x cos( e x ) 8. 100(4 x - x 2 ) 99 (4 - 2 x ) (Power + Chain rule) 18. 12 t 5 ( t + 1)( t 3 + 1) 3 ( t 4 - 1) 2 . (Simplify!) 32. 6 tan(3 θ ) sec 2 (3 θ ) (Chain rule twice.) 40. cos( x ) cos(sin x ) cos(sin(sin x )) HW 16 p. 213 4. y 0 = 2 sin x (5 - cos x ).
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6. y 0 = - 2 y x 16. y 0 = - ± 4 xy 2 x + y - 1 4 x 2 y x + y - 1 ² 46. y 0 = 1 2(1 + x 2 ) p tan - 1 ( x ) HW 17 p. 220 8. f 0 ( x ) = 1 5 x 14. F 0 ( y ) = ye y 1 + e y + ln(1 + e y ) 24. y 0 = x 2 (1 - 2 ln x ) x 3 42. y 0 = x cos x ³ cos x x - ln x · sin x ´ 46. y 0 = (sin x ) ln x ± 1 x ln(sin x ) + (ln x ) · cot x ² HW 18 p. 240 4. (a) Using the given information, solve the two equations for k first. Find k = 1 6 ln 125. Then P (0) = 120. (b) Substitute these values into
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Unformatted text preview: P ( t ) = P (0) e kt . 8. (a) Use formula k =-ln 2 t 1 / 2 , where t 1 / 2 = 5 in this case. Substitute into m ( t ) = 800 e kt to nd the model function: m ( t ) = 800 2-t/ 5 . (b) 12.5 (c) Set m ( t ) = 1 in the model function and solve for t = 48 . 2 days. (d) Graph is decaying exponential, y-intercept 800. 16. The standard heating/cooling model can be written T ( t ) = T s + ( T (0)-T s ) e kt , where T s is the temperature of the surroundings. .. HW 19 HW 20...
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Answers to even-numbered HW - Test 3 - P ( t ) = P (0) e kt...

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