Due Date: October 4, 2011
1.
In your own words, what is instantaneous slope?
2.
Why are the calculations of derivatives in R only approximations?
3.
Plot the function P(t) as given in Lab 6 along with its derivative in the same figure for the following parameters. Don’t forget to round your derivative vector as we did in the lab. Be sure your axes are labeled correctly and you have labeled both plots in your figure. Answer the questions below carefully and completely. Refer to section 1.10 in the book for more information about this system. a.
p0 = .001, s = 2, r = 1.5
Include a jpeg of this figure in your report to turn in and answer the following questions.
Why does the derivative have the shape it does? Be specific about how the shape of the derivative relates to the shape of the P(t). Why is the derivative always ≥ 0? In the end, does the mutant or wild type population win? Why? b.
p0 = .999, s = 1.5, r = 2
Include a jpeg of this figure in your report to turn in and answer the following questions.
Why does the derivative have the shape it does? Be specific about how the shape of the derivative relates to the shape of the P(t). Why is the derivative always ≤ 0? In the end, does the mutant or wild type population win? Why?