# Net greenl

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**Description:** This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential function where C>0 and k is an arbitrarily fixed value in f(x)=Ce^(kx).

- develop their understanding of the effects of the initial value in an exponential function
- exercise their mathematical intuition and verify it via appropriate calculations
- exercise the skills of algebraic and mathematical analysis

This activity can be carried out in either a small College Algebra class or a large lecture setting anytime during or after the topic of graphing exponential functions has been covered.

The activity is comprised of three segments: ConcepTest, Question of the Day and Conclusion, involving the use of a demonstration applet. The time required for the entire activity is approximately 25 minutes but fewer segments can be offered as a shorter alternative (see Activity Description below for individual segment times).

- Instructor presents a ConcepTest (Rich Text File 73kB Aug18 10) in the form of a straw poll (either show-of-hands or written) concerning the effect of increasing the initial value, C, on the position of the y-intercept and the position of the graph with regard to quadrants. Each student is asked to make a conjecture and the instructor records the results for the class to see. (

In addition, the instructor ensures that students understand the algebraic and mathematical analysis involved and clearly explains the reasons for the effects. (

Student understanding of the role of initial value and proportionality constant in exponential functions is limited at best. Most have not considered the y-intercept in terms of the values of C and k, and many have difficulty in analyzing the effects of changing the values of these terms. The fact that using a negative value for k reflects the graph around the y-axis seems to escape them. This activity is designed to help them develop a better grasp of the nature of exponential functions.