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math_final

math_final - Math 151 2010-some nal review questions 1...

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Math 151, 2010 -some final review questions 1. Solve for x. log 8 ( x + 4) = 2 . 2. Assume P(A) = .4 and P(B) = .4 and P(A S B) = .7. Find the P( A T B ) . 3. Suppose a population consists of juveniles and adults, and individuals live for one year in each of these states. Juvenile females produce on average 2 new juvenile fe- male offspring each year, while female adults produce on average 9 juvenile female offspring before the female adult dies. On average, only one third of all juveniles survive to become adults. (5 points each part) a. Write a matrix equation that al- lows you to get J(n) and A(n) given J(0) and A(0) (with J and A representing female juveniles and female adults). b. Suppose there are 10 juvenile females and one female adult present at time 0. How many of each will be present two years later? c. If this population were to exist for a long time, what would its long term growth rate be (using this ‘female’ model)? d. What would be the long-term ratio of female juveniles to female adults in the population?

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