Homework 14

# Homework 14 - Garcia Ilse Homework 14 Due 3:00 am Inst...

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Garcia, Ilse – Homework 14 – Due: Nov 27 2007, 3:00 am – Inst: Fonken 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. The due time is Central time. 001 (part 1 o± 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 a±ter the study began the population size, N ( t ), was increasing at a rate proportional to 1200 - N ( t ). I± the population was 1100 in year 2000, estimate the size o± the elk popula- tion in year 2010? 1. population size 1120 2. population size 1140 3. population size 1180 correct 4. population size 1160 5. population size 1200 Explanation: The population size, N ( t ), satisfes the equations dN dt = k (1200 - N ) , N (0) = 700 with k a constant. Thus - ln(1200 - N ) = kt + C which a±ter exponentiation becomes N ( t ) = 1200 - Ae - kt where A is an arbitrary constant. Now A is determined by the initial condition on N ( t ) because N (0) = 700 = A = 500 . Consequently, N ( t ) = 1200 - 500 e - kt . On the other hand, the value o± k is deter- mined by the population size in year 2000 when N (10) = 1100, ±or then 100 = 500 e - 10 k . Taking logs o± both sides we thus see that k = 1 10 ln 5 · . In year 2010, there±ore, N (20) = 1200 - 500 e - 2 ln 5 . Hence, in year 2010, population size 1180 . keywords: 002 (part 1 o± 1) 10 points An investor buys shares o± a stock ±or \$2000 and sells them 10 years later ±or \$4000. I± in- terest is compounded continuously, determine the annual % rate o± interest that the original \$2000 investment earned, leaving your answer in logarithmic ±orm. 1. interest rate = µ 10 ln 3 2 % 2. interest rate = µ 10 ln 7 4 % 3. interest rate = µ 1 10 ln 9 4 % 4. interest rate = µ 10 ln 9 4 % 5. interest rate = µ 1 10 ln 2 % 6. interest rate = µ 1 10 ln 3 2 % 7. interest rate = (10 ln 2) % correct

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Garcia, Ilse – Homework 14 – Due: Nov 27 2007, 3:00 am – Inst: Fonken 2 8. interest rate = µ 1 10 ln 7 4 %
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## This note was uploaded on 01/16/2009 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.

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Homework 14 - Garcia Ilse Homework 14 Due 3:00 am Inst...

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