Computer Lab Help 12

This page is designed to provide helpful information about the laboratory questions. You will find more details in the Lab Manual that accompanies this course. Begin this lab and every lab by introducing yourself to your partner. Determine the times when you can meet together during the week before the lab is due at your next Lab session. You should start this lab and each lab by typing the name of each team member and your computer number on the Lab Cover Page (or a copy of it).

The first WeBWorK problem asks questions about this help page and appropriate lecture material. This should help you work through the Lab more smoothly. This lab explores three problems using differential equations. The first problem examines a controversy on how E. coli grows in volume using different assumptions. The second problem studies how lead builds up in a child, using techniques similar to the ones developed in lecture. The last problem considers a couple of differential equation models used to determine the population growth of a country.

Problem 1: This question examines two models using relatively simple differential equations. The first one is a simple integration like the cat falling under gravity, while the second one uses a differential equation like the one for Malthusian growth. The only difference from what we have done in class is that you will need to use information on the doubling time to find the constants a and k. That is, you substitute twice the volume at the appropriate time and solve for the unknown. (The constant of integration from solving the differential equations can be obtained from the initial condition.)

In Part c. you want to take the difference between your two solutions. (These solutions should have a difference of zero at times 0 and the cell divide time, since they both should satisfy the same conditions at these times.) Your lab report gives you the form of the function, which can be easily graphed. Use your standard techniques to find the maximum of this function, giving you the greatest error on the interval.

I'll let you think about the Biology of Part d. However, you should think about the magnitude of the error found in Part c and what you know about errors in biological lab experiments. Also, you should remember how models are formulated or the processes involved in cell division.

Problem 2 : This problem is very similar to the ones we have recently done in class on Hg in fish or lead in children. This is a variation on the lead in children problem from the Lecture Notes (Differential Equations and Integration) and the homework problems. Mostly, this problem has you showing your expertise in graphing and solving differential equations that you have learned over the semester to date. There are no special instructions needed for this problem (though I might suggest using the Google search engine with key words lead and children to find more information for the last question).