Chapter 2.1, Problem 32E

Terminal Velocity Revisited In one of the early “Functions and change” pilot courses at Oklahoma State University, the instructor asked the class to determine when in Example terminal velocity would be reached. Three students gave the following three answers:

Student 1: 58 seconds into the fall.

Student 2: 147 seconds into the fall.

Student 3: Never.

Each student’s answer was accompanied by what the instructor judged to be an appropriate supporting argument, and each student received full credit for the problem. What supporting arguments might the students have used to convince the instructor that these three different answers could all be deserving of full credit? (Hint: Consider the formula given in Example 2.1. For student 1, look at a table of values where the entries are rounded to two decimal places. For student 2, look at a table of values made by using all the digits beyond the decimal point that the calculator can handle. In this case, that was nine. For student 3, consider what value ${0.834}^t$ must have to make $176\left(1-{0.834}^t\right)$ equal to 176.)