Discovery of Exponential Function Characteristics

Use the following applet at http://www.pa.uky.edu/~phy211/graph_applets/plot_graph.html to graph the following functions in the form of y = b^x.  Record your graphs and answer the questions.

Graph the following exponential equations.

1.  y = 2^x

a)  y-intercept____________

b)  Increasing or decreasing function?

______________________________

c)  b = ______________

2.  y = 3^x

a)  y-intercept____________

b)  Increasing or decreasing function?

______________________________

c)  b = ______________

3.  y = 5^x

a)  y-intercept____________

b)  Increasing or decreasing function?

______________________________

c)  b = ______________

4.  y = 1^x

a)  y-intercept____________

b)  Increasing or decreasing function?

______________________________

c)  b = ______________

5.  y = (1/2)^x

a)  y-intercept____________

b)  Increasing or decreasing function?

______________________________

c)  b = ______________

6.  y = (1/3)^x

a)  y-intercept____________

b)  Increasing or decreasing function?

______________________________

c)  b = ______________

7.  y = (1/5)^x

a)  y-intercept____________

b)  Increasing or decreasing function?

______________________________

c)  b = ______________

8.  What point do they all have in common?________________

9.  List the equations that are increasing?_______________________________________

10.  List the equations that are decreasing?_____________________________________

11.  What is the relationship between the graphs of equations 1 and 5, 2 and 6 and 3 and 7?______________________________________________________________________

12.  Exponential graphs that are increasing show exponential growth.  What are the similarities of all the equations that produce such graphs?

_____________________________________________________________________

_____________________________________________________________________

13.  Exponential graphs that are decreasing show exponential decay.  What are the similarities of all of the equations that produce such graphs?

______________________________________________________________________

_______________________________________________________________________

14.  Are there any graphs which are not reflecting exponential growth or decay?  Why?

________________________________________________________________________

________________________________________________________________________

This worksheet was adapted from Exploring Exponential Growth and Decay Functions by Sharon Nussbaum, Jessica Redlin, and Denise Stewart