2. Exponential Functions
The general form of an exponential function is
where x is a real number, a ≠ 0, b > 0, and b ≠
1.
To graph an Exponential Function: create a
table of values and plot the points
Example: Graph
3. Exponential Functions
Exponential Functions always have the curved
shape
They also have an asymptote, a line that the
graph approaches but never touches or
crosses The domain is all real
numbers.
The range is y > 0
4. Exponential Functions
There are two types of exponential behavior
Exponential Exponential Decay
Growth As the value of x
As the value of x increases, the value
increases, the value of y decreases
of y increases
5. Exponential Functions
For the function
If a > 0 and b >1, the function represents
exponential growth
If a > 0 and 0 < b < 1, the function represents
exponential decay
The y-intercept of the graph is at (0, a)
The asymptote is y = 0
6. Without graphing, determine whether the function
represents exponential growth or decay. Then find
the y-intercept.
7. Exponential Growth and Decay
In the function , b represents the growth
or decay factor.
If b > , then it is the growth factor
If 0 < b < 1, then it is the decay factor
8. Exponential Growth and Decay
To model exponential growth and decay we use
the following function To use this
function:
1. Identify the
value of the
variables
2. Plug the known
values into the
equation
3. Solve for the
For growth or decay to be exponential,unknown value
a quantity
changes by a fixed percentage each time period
9. Example: Page 436
You invested $1000 in a savings account at
the end of the 6th grade. The account pays 5%
annual interest. How much money will be in
the account after 6 years?
10. Homework
P. 439 #1 – 6 all, 8, 10 – 25 odd, 26 (parts a &
b), 27, 28
