Pre-Calc Homework Solutions 259

Pre-Calc Homework Solutions 259 - Section 6.4 5. 0.85x ln...

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5. 0.85 x 5 2.5 ln 0.85 x 5 ln 2.5 x ln 0.85 5 ln 2.5 x 5 } l l n n 0 2 . . 8 5 5 } < 2 5.638 6. 2 k 1 1 5 3 k ln 2 k 1 1 5 ln 3 k ( k 1 1)ln 2 5 k ln 3 ln 2 5 k (ln 3 2 ln 2) k 5 } ln 3 ln 2 2 ln 2 } < 1.710 7. 1.1 t 5 10 ln 1.1 t 5 ln 10 t ln 1.1 5 ln 10 t 5 } l l n n 1 1 . 0 1 } 5 } log 1 1.1 } < 24.159 8. e 2 2 t 5 } 1 4 } 2 2 t 5 ln 1 } 1 4 } 2 t 52} 1 2 } ln 1 } 1 4 } 2 5 } 1 2 } ln 4 5 ln 2 9. ln ( y 1 1) 5 2 x 1 3 y 1 1 5 e 2 x 1 3 y 52 1 1 e 2 x 1 3 10. ln ) y 1 2 ) 5 3 t 2 1 ) y 1 2 ) 5 e 3 t 2 1 y 1 2 56 e 3 t 2 1 y 2 6 e 3 t 2 1 Section 6.4 Exercises 1. y ( t ) 5 y 0 e kt y ( t ) 5 100 e 1.5 t 2. y ( t ) 5 y 0 e kt y ( t ) 5 200 e 2 05 t 3. y ( t ) 5 y 0 e kt y ( t ) 5 50 e kt y (5) 5 100 5 50 e 5 k 2 5 e 5 k ln 2 5 5 k k 5 0.2 ln 2 Solution: y ( t ) 5 50 e (0.2 ln 2) t or y ( t ) 5 50 ? 2 0.2 t 4. y ( t ) 5 y 0 e kt y ( t ) 5 60 e kt y (10) 5 30 5 60 e 10 k } 1 2 } 5 e 10 k ln } 1 2 } 5 10 k k 5 0.1 ln } 1 2 }52 0.1 ln 2 Solution: y ( t ) 5 60 e 2 (0.1 ln 2) t or y ( t ) 5 60 ? 2 2 t /10 5. Doubling time: A ( t ) 5 A 0 e rt 2000 5 1000 e 0.086 t 2 5 e 0.086 t ln 2 5 0.086 t t 5 } 0 l . n 08 2 6 } < 8.06 yr Amount in 30 years: A 5 1000 e (0.086)(30) < $13,197.10 6. Annual rate: A ( t ) 5 A 0 e rt 4000 5 2000 e ( r )(15) 2 5 e 15 r ln 2 5 15 r r 5 } l 1 n 5 2 } < 0.0462 5 4.62% Amount in 30 years: A ( t ) 5 A 0 e rt A 5 2000 e [(ln 2)/15](30) 5 2000 e 2 ln 2 5 2000 ? 2 2 5 $8000 7. Initial deposit: A ( t ) 5 A 0 e rt 2898.44 5 A 0 e (0.0525)(30) A 0 5 } 28 e 9 1.
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