SDSU

Math 121 Calculus for Biology
Spring Semester, 2007
Lab Help

Feb-23

San Diego State University


Laboratory Help Page for Lab 4

The first problem introduces the exponential and logarithm functions.
The second problem covers the material on the Allometric Models.


Question 1 (E1): This problem compares the relative rate of growth of exponential functions to power functions and logarithmic functions to fractional power functions. You will be finding points of intersection for these graphs using Maple's fsolve command. You are given two intervals to aid your search for the points of intersection. As you did before, you first create the graph, then use the information that you glean from the graph to help you find the points of intersection (i.e., you restrict the range you search with fsolve for these points of intersection. Your lab report can have your graphs in either Maple or Excel, but in either case, make sure that you clearly label which graph is which. The only new Maple command that you will need is that exp(x) is used to give you ex (remember that the natural logarithm is given by ln(x)). The key to finding the dominance of one function over the other (the intervals where f(x) < g(x) or vice versa) is simply to find the points of intersection, then observe which function is higher than the other between two successive points of intersection. (They will swap positions on the next interval between points of intersection.) This part of the question is asking you to interpret the graphs of the functions.


Question 2 (E2): This problem is very similar to the one we saw in class. The problem addresses the issue of biodiversity and the amount of land required to maintain a certain level of biological diversity. The model you produce gives a more quantitative answer to how much land is required, using Excel's power law.