Math 464, Handout 1
1. Suppose that in a population of 100 animals the probabilities of death and birth are pd= 0.02
per day and pb= 0.05 per day. Choose a suitable time interval and then:
(a) Find the (expected) population at the end of each of the next five weeks.
(b) Find the (expected) population at the beginning of each of the previous five 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.
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 A0animals 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 napproaches infinity.
6. With A0= 100, compute the population at times t= 35 days and −35 days. Compare to
your answers from Exercise 1.
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