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, Oct. 27. If your schedules are totally incompatible, then notify me immediately.

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 examines the growth the the World population using a simple Malthusian growth model. In this case, we use the continuous Malthusian growth model rather than the discrete version learned earlier in the semester. You begin by solving the Malthusian growth model using Maple's dsolve routine. This routine will allow you to solve a variety of differential equations. The commands are simply:

> de := diff(P(t),t)= r*P(t);
> dsolve({de, P(0) = P0}, P(t));

The solution to this differential equation is an exponential function that we want to fit to the data. You fit the data using Excel's Trendline, as you have done before, but you choose the exponential fit to find the best fit to these data. You will also make a graph of the data and the model with a logarithmic vertical axis or the semilog plot. You can do this by simply copying the previous graph on your worksheet, then double clicking on the vertical axis and checking the logarithic scale under the scale category. The remainder of the questions are simply using the formula that Excel finds for you to make predictions and perform error analysis of the model.

Question 2: This is an exercise to help you understand radioactive decay. The lecture notes give the solution to the basic radioactive decay problem, and this question uses that solution to date ancient objects. The techniques developed in class and the lecture notes provide all the basic material for this problem. About the only difference is the computing of bounds in age based on the error in readings of dpm and using the bounds on the age in Part e to find the error in the dpm readings. You can do each of these by simply putting in the extreme numbers. For example, if your object had a reading of 10.14 ± 0.3 dpm, then look at the ages from readings of 10.44 and 9.84. Similarly, in Part e. if the object has an age of 2,153 ± 200, you should find the expected readings in dpm from ages of 1953 and 2353 years old.