ws01-1 - 3. Using the same time interval and birth/death...

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Math 464, Handout 1 1. Suppose that in a population of 100 animals the probabilities of death and birth are p d = 0 . 02 per day and p b = 0 . 05 per day. Choose a suitable time interval and then: (a) Find the (expected) population at the end of each of the next ±ve weeks. (b) Find the (expected) population at the beginning of each of the previous ±ve weeks. (c) Graph your results. Be sure to label your axes clearly. (d) Find a formula for (expected) population as a function of time, t , in days. 2. Using the same time interval and birth/death probabilities, repeat Exercise 1 with an initial population of 50 animals. Draw your graph on the same axes as in Exercise 1.
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Unformatted text preview: 3. Using the same time interval and birth/death probabilities, repeat Exercise 2 with an initial population of 150 animals. Draw your graph on the same axes as in Exercise 1. 4. Assume an initial population of A animals with birth/death probabilities as above. Find a formula for population as a function of time with the time step set at 1 /n days. 5. Take the limit as n approaches innity. 6. With A = 100, compute the population at times t = 35 days and-35 days. Compare to your answers from Exercise 1. 1...
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This note was uploaded on 10/12/2011 for the course MATH 464 taught by Professor Dougbullock during the Fall '08 term at Boise State.

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