Math 31L.13
Calculus I with Environmental Emphasis

Fall 1997

Plan for Week 3

At the end of Week 2 we found that important examples of inverse functions include the logarithm functions, which are the inverses of exponential functions with the same base. In particular, the inverse of the base-10 exponential function,

y = 10x,

is the common logarithm function,

y = log x.

This function is important enough to have its own key on your calculator.

We begin this week with an activity that puts this log function to work in a graphical context that enables us to determine whether given data can reasonably be fitted by a power function or an exponential function (or neither of these). This week's lab is based on this logarithmic graphing concept.

On Wednesday we will address some of the issues that arise in using writing as a tool for learning mathematics. In preparation for that class, you should review the online Guide to Writing. We will use anonymous samples from writing you have done already in this course.

While our activities focus on the (possibly new) topics of logarithmic graphing and writing, your reading and homework assignments will deal with additional review of precalculus topics:

At the end of the week, we start on our first calculus topic, instantaneous rate of change. We will see that this idea flows very naturally from average rate of change, such as the average speed necessary to travel a certain distance in a certain time. By considering very small time intervals, we can examine speed at an instant.

Here is the syllabus for Week 3:

Week 3 Date Topic Reading Activity
M 9/15 New functions from old 1.9 Log plots
W 9/17 Polynomial and rational
functions		 1.11,
Guide to
Writing
 Writing day
Th 9/18 Logarithmic plotting Lab: Radioactive Decay
F 9/19 Speed and velocity 2.1

Notes

  1. Your next homework papers will be turned in on Monday, September 22. Those papers should include solutions to the problems whose numbers are boldfaced italics in the assignment below. The assignment dates are start dates.
  2. Observe that our syllabus postpones sections 1.7 and 1.10 until Weeks 4 and 8, respectively, and omits 1.8 entirely. This is so we can get on to calculus sooner. The postponed topics are more meaningful in a calculus context, and the ideas in 1.8 will be treated in other ways, primarily in labs.
  3. Remember to submit your weekly journal entry by e-mail on or before Friday, September 19.

Assignments

David A. Smith <das@math.duke.edu>

Last modified: September 11, 1997