This lab continues the study of applications of the derivative. Again you will find Maple useful to help solve these problems. The first problem parallels the work we did in lecture on the variation of body temperature of a human female over her menstrual cycle. The second problem examines two drug treatment regimes.  The last problem has you fitting data on radioactive materials used in biomedical imaging. 

Question 1: This problem examines the variation of the female body temperature over the period of a month. A cubic polynomial is fit to data, then the maximum and minimum are found. The point of inflection corresponds to the maximum increase in temperature, which also matches the point of ovulation or greatest fertility. This is a classic use of differential Calculus and follows the notes in the text. The problem uses Excel's Trendline with the polynomial curve fitting algorithm. The derivatives are most easily found with Maple, which allows easy computation of the minimum, maximum, and point of inflection.

Question 2: In this problem consider a decaying exponential and the difference of two decaying exponentials. This parallels the study of Prozac in the lecture notes. The exponentially decaying amount of drug is a problem you might want to practice by hand, as it is similar to problems that will arise in exams. The pharmacologial equation is used for drugs that arise from metabolism of one drug into another form with the difference of two decaying exponentials. The second drug concentration requires differentiating exponentials to find the maximum. You can have Maple help you with this or practice the techniques by hand. The most difficult part is trying to find when the second drug level is at some threshold level. This is most easily done using Maple's fsolve command. Note that you will need to find the first time when the drug becomes effective, then subtract this time from the time when the drug loses efficacy due to exponential decay. Graphing the function can help narrow the range where you use Maple's fsolve command. The computer methods are very similar to ones that you have already been using.

Question 3: This problem examines two radioactive isotopes that are used in medical imaging. The first isotope simply decays exponentially and is fit with Excel's Trendline with the exponential fit. The second isotope's data are fit using the difference of two decaying exponentials. One decay rate comes from the analysis of the first part of the problem. The other two parameters are fit to the data with Excel's Solver, obtaining the other decay rate and the constant multiplying the exponentials. This maximum and point of inflection can be done by hand or you can use Maple to find the values more quickly. Again the techniques for this problem are similar to the ones using Excel's Trendline and Solver and Maple, as you have done in the past. No new computer techniques are introduced.