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MarcKrishkeMath1600Project10

MarcKrishkeMath1600Project10 - 10 20 200 36450 675 4050 450...

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Chapter 10: Applications of Derivatives
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(a) The hotel’s occupancy rate at the beginning of January (t = 0) is 3 2 10 10 200 (0) 0 0 0 55 55 81 3 9 r = - + + = The hotel’s occupancy rate at the beginning of June ( t = 5) is 3 2 10 10 200 (5) 5 5 5 55 98.21 81 3 9 r = - + + =
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(b) The hotel’s monthly revenue at the beginning of January (t = 0) is 3 2 3 9 ( (0)) (55) 55 55 444.675 5000 50 R r R = = - + = The hotel’s monthly revenue at the beginning of June (t = 5) is 3 2 3 9 ( (5)) (98.21) 98.21 98.21 1167.78 5000 50 R r R = = - + = (c) 2 2 10 10 200 10 20 200 3 2 81 3 9 27 3 9 dr t t t t dt = - + = - + (d) 2 2 3 9 9 9 3 2 5000 50 5000 25 dR r r r r dr = - + = - + 2 2 2 3 2 3 2 2 9 9 10 20 200 5000 25 27 3 9 9 10 10 200 9 10 10 200 10 20 200 55 55 5000 81 3 9 25 81 3 9 27 3 9 dR dR dr r r t t dt dr dt t t t t t t t t  = = - + - +     = - - + + + - + + - +     6 5 4 3 2 3 2 2 9 100 200 12100 10900 10300 2200 2 6 99 3025 8 5000 6561 243 729 81 81 9 45 5 5 10 20 200 27 3 9 t t t t t t t t t t t = - - + - - + + + - + + - + 6 5 4 3 2 3 2 2 1 1 121 109 103 22 1089 2 6 99 8 36450 675 4050 450 450 5 200 45 5 5 10 20 200 27 3 9 t t t t t t t t t t t = - + - + - - - + - + + - + 6 5 4 3 2 2 1 1
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Unformatted text preview: 10 20 200 36450 675 4050 450 450 5 200 27 3 9 t t t t t t t t = -+-+-+ +-+ 8 7 6 5 4 3 2 1 8 707 137 2263 2326 81707 157 319 98415 10935 32805 405 729 135 1620 10 t t t t t t t t = -+-+-+--+ (e) The rate of change of monthly revenue at the beginning of January (t = 0) is 8 7 6 5 4 3 2 1 8 707 137 2263 2326 81707 98415 10935 32805 405 729 135 1620 157 319 319 10 t dR dt = = - + - + - + -- + = The rate of change of monthly revenue at the beginning of June (t = 5) is 8 7 6 5 4 3 2 5 1 8 707 137 2263 2326 81707 5 5 5 5 5 5 5 98415 10935 32805 405 729 135 1620 157 5 319 33.32 10 t dR dt = = - + - + - + -- + = -...
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