# HW 14 - Tran, Tony – Homework 14 – Due: Nov 27 2007,...

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Unformatted text preview: Tran, Tony – Homework 14 – Due: Nov 27 2007, 3:00 am – Inst: Samuels 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Scientists began studying the elk popula- tion in Yellowstone Park in 1990 when there were 400 elk. They determined that t years after the study began the population size, N ( t ), was increasing at a rate proportional to 1000- N ( t ). If the population was 500 in year 2000, estimate the size of the elk population in year 2010? 1. population size ≈ 544 2. population size ≈ 564 3. population size ≈ 584 correct 4. population size ≈ 524 5. population size ≈ 504 Explanation: The population size, N ( t ), satisfies the equations dN dt = k (1000- N ) , N (0) = 400 with k a constant. Thus- ln(1000- N ) = kt + C which after exponentiation becomes N ( t ) = 1000- Ae- kt where A is an arbitrary constant. Now A is determined by the initial condition on N ( t ) because N (0) = 400 = ⇒ A = 600 . Consequently, N ( t ) = 1000- 600 e- kt . On the other hand, the value of k is deter- mined by the population size in year 2000 when N (10) = 500, for then 500 = 600 e- 10 k . Taking logs of both sides we thus see that k = 1 10 ln ‡ 6 5 · . In year 2010, therefore, N (20) = 1000- 600 e- 2 ln 6 5 . Hence, in year 2010, population size ≈ 584 . keywords: 002 (part 1 of 1) 10 points An investor buys shares of a stock for \$4000 and sells them 5 years later for \$6000. If in- terest is compounded continuously, determine the annual % rate of interest that the original \$4000 investment earned, leaving your answer in logarithmic form. 1. interest rate = µ 1 5 ln 13 8 ¶ % 2. interest rate = µ 20ln 13 8 ¶ % 3. interest rate = µ 1 5 ln 11 8 ¶ % 4. interest rate = µ 1 5 ln 5 4 ¶ % 5. interest rate = µ 20ln 11 8 ¶ % 6. interest rate = µ 20ln 3 2 ¶ % correct 7. interest rate = µ 20ln...
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## This note was uploaded on 04/27/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas at Austin.

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HW 14 - Tran, Tony – Homework 14 – Due: Nov 27 2007,...

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