Textbook 8.2
Objective:
a. Graph exponential decay functions.
b. Use exponential growth functions to model real-life situations.
Exponential decay functions have the form ( )
Sample: ( )
where a>0 and 0<b<1.
( )
How would you describe the end behaviors of the function?
As x
As x
-, f(x)
+, f(x)
______.
______, which means y = 0 is an _______________________.
Recall: characteristics of an exponential function,
:
1) the graph passes through the point (________); the y-intercept is ____.
2) the ________________ is an asymptote of the graph.
3) the domain is all real numbers.
4) the range is y > 0 if a > 0 and y < 0 if a < 0.
Exponential Decay
Example 1:
Graph
y
( )
Step 1) plot (0, 3)
Step 2) plot (1, 3/4)
Step 3) draw the curve
- start with asymptote
- include two points
- end behavior
x
Example 2:
Graph
y
( )
Step 1) plot (0, -5)
x
Step 2) plot (1, -10/3)
Step 3) draw the curve
- start with asymptote
- include two points
- end behavior
Example 3: Graph
( )
. State the domain and range.
y
x
Decay Factor
When using exponential functions to model real-life situations, the equation
(
)
a is the _____________________________
r is the _____________________________ (a decimal value)
1 - r is the _________________________________
Example 4: You buy a new car for $24,000. The value y of the car decreases by 16% each year.
a. Write an exponential decay model for the value of the car. Use the model to estimate the value
after 2 years.
b. Graph the model.
c. Use the graph to estimate when the car will have a value of $12,000.