Laboratory Help Page

This page is designed to provide helpful information about the laboratory questions.

Begin this lab and every lab by introducing yourself to your partner. Detemine the times when you can meet together during the week before the lab is due on Friday, Sept. 15. If your schedules are totally incompatible, then notify me immediately.

Log onto the computer and download the Cover Page, Summary Page, Graphing Template, and Discrete Template. You will probably want to download your specific lab page (and may want to convert it to a Word document). On the cover page you begin by typing in the name of each team member and your group number.

Question 1: This question is designed to get you familiar with Maple. There will be a special Maple help sheet that should give all the primary commands that you need. (We will cover this at the beginning of the Lab.) It will help you for the classroom material if you do some of the calculations by hand. However, some of the calculations such as the intercepts and the points of intersection are too difficult to be done by hand. Maple will handle these computations very efficiently, and hopefully give you a better understanding of the material. (Note that the primary help for this question is provided by the Maple help sheet, which I recommend you keep easily available for the rest of the semester, adding the new commands that you learn.) Be sure to limit the range of the graph also to make points of intersection clear in your graphs.

Question 2: This problem reviews Malthusian growth and extends this modeling to a nonlinear model showing the fraction of the total population that is of a certain strain. As noted in the problem, these calculations can be very important in examining how mutations affect an experiment. Part a. of this problem is one that should be able to be done by hand. It will provide you with a good review of this type of problem as it is a likely candidate for the upcoming Quiz. The second part is easily performed in Excel. You probably want to enter 0 in A1, A₀ in B1, and B₀ in C1. Compute P₀ from A₀ and B₀, using the given formula and enter it into D1. (If you want to label your cells, then shift these down by one.) On your spreadsheet in A2, you'll enter =A1+1. In B2, you enter =(1+r)*B1. (Similar for C2.) In D2, you'll enter = (1+r)*D1/(1 + s + (r - s)*D1). Then you'll simply fill down and read off the appropriate values. Finally, in the last part, you can probably do most of the work by hand (though if you like Maple, it can help you, especially for the stability argument). The graph that you want can easily use the graphing template sheet listed above.

Question 3: This problem works with real data on Paramecium. This again is an Excel problem. You want to start by putting the populations from days 0-11 in column A. Next you put the populations from days 1-12 in column B. You graph these two columns using scatter plot in Excel (which you should have done before). Leave these as data points clearly distinct on the graph. Next you use the Trendline polynomial fit as instructed in the Lab question. For Part b, you want to choose 3other columns. In the first column, enter the data for the day number. In the second column, enter the population data. In the third column, you first enter the starting population, then just as you did in Question 2, you enter the formula (as Part a. for the formula) and fill down. You can easily graph these 3 columns for your result. Use points on the graph for data and lines for the theoretical model.