Download 10.1 Exponential Functions

10.1
Exponential
Functions
2)
Objectives: The student will be able to…
1) Graph exponential functions.
Solve exponential equations and inequalities.
Example 1
x
y
Exponential Functions
•
•
•
•
•
•
Take the form y = abx
Base (b) is a constant
Exponent is a variable
Example: y = 2 x
a=
b=
The x-axis is an asymptote of the general graph.
The graph contains the point (0, a).
Two Types of Exponential Functions
Exponential Growth
Exponential Decay
- Base is a number greater than 1
-base is a number between 0 and 1
You Try It…
Sketch a graph of the exponential function. Then state the
domain and range. Indicate if it is a growth or decay.
Example 2
Determine whether each function represents
exponential growth or decay.
a)
æ1ö
y =ç ÷
è 5ø
x
b) y = 3(4)x
c) y = 7(1.2)x
Word Problems!
Text p. 528
Text p. 529
Text p. 525
Homework
Text p. 528 #s 19-32 all
#s 59-61
Exponential Equations and Inequalities
• Since the domain of an exponential function
includes irrational numbers such as 2 , all
the properties of rational exponents apply
to irrational exponents.
Example 4:
Simplify each expression:
You Try It…
Simplify each exponential expression:
Property of Equality
for Exponential Functions
If b is a positive number other than 1,
then bx = by if and only if x = y.
Example: If 2x = 28, then x = 8
Example 5: Solve each equation
Example 6: Solve the inequality
You Try It…
Solve each exponential equation or inequality.
Homework
Text p. 528 #s 39-55 odd
#s 57-58