1. Mathematics
2. Consumer Mathematics
3. Fractions and Percentages
4. 568035

Do the following dynamic simulation problem:

1. The following model is proposed to describe population growth in a confined space. The excess of births over natural deaths causes a growth rate of a times the current number of individuals N. Competition for food causes deaths from starvation at a rate of bN^2 . Simulate the population growth assuming:
a. a = 0.05
b. b = 0.00001
c. N = 500 at time t=0

2. Assume in problem 1 that a second species exists in the same space subject to a1=0.04, b1=0.000015, and N1=1,000 at time t=0. However interspecies fighting causes deaths to both species at a rate that is 0.000001 times the product of their numbers (0.000001N(N1) ). Extend the model to plot the population dynamics for both species.