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Pre-Calc Homework Solutions 267

Pre-Calc Homework Solutions 267 - M 5 100 8 5 P d d P t 5 2...

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10. } x 2 2 x 1 1 x 1 2 6 6 } 5 } x 1 A 3 } 1 } x 2 B 2 } 2 x 1 16 5 A ( x 2 2) 1 B ( x 1 3) When x 5 2 3, the equation becomes 10 5 2 5 A , and when x 5 2, the equation becomes 20 5 5 B . Thus, A 5 2 2 and B 5 4. Section 6.5 Exercises 1. (a) } d d P t } 5 0.025 P (b) Using the Law of Exponential Change from Section 6.4, the formula is P 5 75,000 e 0.025 t (c) [0, 100] by [0, 1,000,000] 2. (a) } d d P t } 5 0.019 P (b) Using the Law of Exponential Change from Section 6.4, the formula is P 5 110,000 e 0.019 t . (c) [0, 100] by [0, 1,000,000] 3. (a) } d d P t } 5 } M k } P ( M 2 P ) } d d P t } 5 } 0 2 . 0 0 0 5 } P (200 2 P ) } d d P t } 5 0.00025 P (200 2 P ) (b) P 5 } 1 1 M Ae 2 kt } P 5 } 1 1 2 A 0 e 0 2 0.05 t } Initial condition: P (0) 5 10 10 5 } 1 1 20 A 0 e 0 } 1 1 A 5 } 2 1 0 0 0 } 5 20 A 5 19 Formula: P 5 } 1 1 1 2 9 0 e 0 2 0.05 t } (c) [0, 100] by [0, 250] 4. (a) } d d P t } 5 } m k } P ( M 2 P ) } d d P t } 5 } 0 1 . 5 0 0 2 } P (150 2 P ) } d d P t } 5 } 75 1 00 } P (150 2 P ) (b) P 5 } 1 1 M Ae 2 kt } P 5 } 1 1 1 A 5 e 0 2 0.02 t } Initial condition: P (0) 5 15 15 5 } 1 1 15 A 0 e 0 } 1 1 A 5 } 1 1 5 5 0 } 5 10 A 5 9 Formula: P 5 } 1 1 1 9 5 e 0 2 0.02 t } (c) [0, 200] by [0, 200] 5. The growth rate is 2 0.3 or 2 30%. 6. The growth rate is 0.075 or 7.5%. 7. } d d P t } 5 0.04 P 2 0.0004 P 2 5 0.0004 P (100 2 P ) 5 } 0 1 . 0 0 0 4 } P (100 2 P ) 5 } M k } P ( M 2 P ) Thus, k 5 0.04 and the carrying capacity is M 5 100. 8. } 5 P 0 }
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Unformatted text preview: M 5 100. 8. } 5 P } } d d P t } 5 2 2 } 2 P 50 } } P 1 } } d d P t } 5 } 5 1 } 1 2 2 } 2 P 50 } 2 5 } 2 1 5 } 1 1 2 } 5 P 00 } 2 5 0.04 1 1 2 } 5 P 00 } 2 5 k 1 1 2 } M P } 2 Thus, k 5 0.04 and the carrying capacity is M 5 500. 9. Choose the slope field that shows slopes that increase as y increases. (d) 10. Choose the slope field that matches a logistic differential equation with M 5 100. (b) 11. Choose the only slope field whose slopes vary with x as well as with y . (c) 12. Choose the slope field that matches a logistic differential equation with M 5 150. (a) Section 6.5 267...
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