Pre-Calc Homework Solutions 272

Pre-Calc Homework Solutions 272 - 272 Section 6.6 dp dt dp...

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Unformatted text preview: 272 Section 6.6 dp dt dp p 32. (a) k(t)p k(t) dt t s Section 6.6 Numerical Methods (pp. 350356) Quick Review 6.6 ln p 0 k(u) du t C p p eCe 0 t k(u) du 1. f (x) f (2) 2. L(x) 3x 2 3 3(2)2 3 9 2) Ae 0 k(u) du f (2) f (2)(x 2 9(x 2) 9x 16 sec2 x sec2 f 1 2x 4 Initial condition: p(0) 0 p0 . p0 p0 p0 Ae 0 Ae A 0 k(u) du 3. f (x) f 4 ( 2)2 f x 2 t 4. L(x) Solution: p(t) 9 9 p0e k(u) du 0 4 4 4 2 4 2x 1 (b) 0 k(u) du 0 0.04 du 1 u 9 0.04 ln (1 0.04(ln 10 0.04 ln 10 9 u) 0 5. f (x) f (4) 6. L(x) 0.2x 5x 2 0.2(4) 5(4) 2 0.4875 ln 1) f (4) f (4)(x 4) 2.85 0.4875(x 4) 0.4875x 0.9 0.4875(4.1) 0.1(4.1)2 f (4.1) 0.9 5 4.1 p(9) p0 e 0 k(u) du 7. L(4.1) 109.65 f (4.1) 2.89875 2.900512 100e0.04 ln 10 After 9 years during which the inflation rate is 0.04 per year, the price of an item which originally 1 t (a) L(4.1) (b) 0.001762 0.00061 0.9 5 4.2 L(4.1) f (4.1) f (4.1) 0.061% cost $100 will be increased to $109.65. 9 8. L(4.2) 100e 0.04(9) 0.4875(4.2) 0.1(4.2)2 f (4.2) 2.9475 2.954476 (c) p(9) p0e 0.04 du 0 143.33 f (4.2) The price will be $143.33. 9 9 (a) L(4.2) (b) 0.522 0 0.006976 0.00236 0.9 5 4.5 (d) 0 k(u) du 0 (0.04 0.04u 9 0.004u) du 0.002u2 9 L(4.2) f (4.2) f (4.2) 0.236% 9. L(4.5) f (4.5) 0.4875(4.5) 0.1(4.5) 2 3.09375 3.136111 p(9) 33. (a) P 2 p0 e kP2 k(u) du 0 100e 0.522 168.54 dP dt (a) L(4.5) (b) f (4.5) 0.042361 0.01351 0.9 5 3.5 dP 1 k dt kt kt L(4.5) f (4.5) f (4.5) 1.351% P C 1 C 10. L(3.5) f (3.5) P0 0.4875(3.5) 0.1(3.5)2 f (3.5) 2.60625 2.653571 P Initial condition: P(0) P0 C 1 C 1 P0 kt (a) L(3.5) (b) 0.047321 0.01783 1.783% L(3.5) f (3.5) f (3.5) Solution: P 1 (1/P0) P0 1 kP0t 1 kP0 (b) There is a vertical asymptote at t ...
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