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Unformatted text preview: Jolley, Garrett Homework 14 Due: Nov 27 2007, 3:00 am Inst: R Heitmann 1 This printout should have 10 questions. Multiplechoice 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 = 1 10 ln 4 3 % 2. interest rate = 10ln 5 4 % 3. interest rate = 1 10 ln 17 12 % 4. interest rate = 10ln 4 3 % correct 5. interest rate = 1 10 ln 7 6 % 6. interest rate = 1 10 ln 5 4 % 7. interest rate =...
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 Spring '08
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