Problem Set 3—Exponential Functions

Purpose

This problem set reinforces your understanding of exponential functions and their derivatives and antiderivatives. It also further develops your understanding of certain logarithmic functions.

Background

This exercise is based on material in section 7.3 of our textbook. We will discuss this material in class on January 28 and 29.

Activity

Solve each of the following problems:

Problem 1

Exercise 2a in section 7.3 of our textbook (solve e^-0.01t = 1000 for t).

Problem 2

Exercise 6 in section 7.3 of our textbook (differentiate e^2x/3).

Problem 3

Exercise 58 in section 7.3 of our textbook (differentiate 2^(x2)).

Problem 4

Exercise 34 in Section 7.3 of our textbook (integrate 2e^2x-1).

Problem 5

Exercise 138 in Section 7.3 of our textbook (find the area between the graph of y = 2^1-x and the interval of the x axis between -1 and 1).

Problem 6

Exercise 140 in Section 7.3 of our textbook (determine whether x^ln 2 and 2^ln x are the same function). As requested in the book, use your favorite graphing calculator or software to investigate the problem graphically, but also give an analytical justification for your answer.

Follow-Up

I will grade this exercise in a face-to-face meeting with you. During this meeting I will look at your solution, ask you any questions I have about it, answer questions you have, etc. Please bring a written solution to the exercise to your meeting, as reading through it will help me know what to focus on in the rest of the meeting.

Sign up for a meeting via Google calendar. If you worked in a group on this exercise, the whole group should schedule a single meeting with me. Please make the meeting 15 minutes long, and schedule it to finish before the end of the “Grade By” date above.

My basic expectation in grading this exercise is that your solution will show that you understand how to solve each problem, although there may be arithmetic or copying mistakes, inefficient solution methods, incorrect or irrelevant statements incidental to the solution, or similar minor mistakes. If you understand how to solve all the problems and have no minor errors, I will consider the solution to be in between “what I expect” and “surprisingly beyond expectations.” I will consider solutions to be 3/4, 1/2, 1/4, or none of what I expect according to what (rough) fraction of the problems your solution shows understanding of, although I will raise grades slightly if it is clear by the end of your grading meeting that you have come to understand things you didn’t understand when you arrived at the meeting.