# HW14 - Jolley Garrett – Homework 14 – Due 3:00 am –...

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Unformatted text preview: Jolley, Garrett – Homework 14 – Due: Nov 27 2007, 3:00 am – Inst: R Heitmann 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 700 elk. They determined that t years after the study began the population size, N ( t ), was increasing at a rate proportional to 1700- N ( t ). If the population was 900 in year 2000, estimate the size of the elk population in year 2010? 1. population size ≈ 1100 2. population size ≈ 1060 correct 3. population size ≈ 1080 4. population size ≈ 1040 5. population size ≈ 1120 Explanation: The population size, N ( t ), satisfies the equations dN dt = k (1700- N ) , N (0) = 700 with k a constant. Thus- ln(1700- N ) = kt + C which after exponentiation becomes N ( t ) = 1700- Ae- kt where A is an arbitrary constant. Now A is determined by the initial condition on N ( t ) because N (0) = 700 = ⇒ A = 1000 . Consequently, N ( t ) = 1700- 1000 e- kt . On the other hand, the value of k is deter- mined by the population size in year 2000 when N (10) = 900, for then 800 = 1000 e- 10 k . Taking logs of both sides we thus see that k = 1 10 ln ‡ 5 4 · . In year 2010, therefore, N (20) = 1700- 1000 e- 2 ln 5 4 . Hence, in year 2010, population size ≈ 1060 . keywords: 002 (part 1 of 1) 10 points An investor buys shares of a stock for \$6000 and sells them 10 years later for \$8000. If in- terest is compounded continuously, determine the annual % rate of interest that the original \$6000 investment earned, leaving your answer in logarithmic form. 1. interest rate = µ 1 10 ln 4 3 ¶ % 2. interest rate = µ 10ln 5 4 ¶ % 3. interest rate = µ 1 10 ln 17 12 ¶ % 4. interest rate = µ 10ln 4 3 ¶ % correct 5. interest rate = µ 1 10 ln 7 6 ¶ % 6. interest rate = µ 1 10 ln 5 4 ¶ % 7. interest rate =...
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HW14 - Jolley Garrett – Homework 14 – Due 3:00 am –...

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