8-1 Exploring Exponent Models
Objectives:
To identify exponential growth and decay.
To define the asymptote
To graph exponential functions
To find the percent increase or decrease.
Exponential Function
A function with the general form y = abx,
where x is a real number, a ≠ 0, b > 0 and b
≠ 1.
example: y = 4(2)x
Growth Factor
 When b > 1, b is the growth factor
example: y = 2(3)x
b = 3 which is greater than 1 so it is the
growth factor and the function is one of
exponential growth.
Decay Factor
 When b < 1, b is the decay factor
example: y = 2(¼)x
b = ¼ which is less than 1 so it is the
decay factor and the function is one of
exponential decay.
Asymptote
 A line that a graph approaches as x or y
increases in absolute value.
Graphing
Example: Graph y = 2x.
make a table
x
2x
-3
2-3
1
8
-2
2-2
1
4
-1
2-1
1
2
0
20
1
1
21
2
2
22
4
3
23
8
y
Percent Increase or Decrease
 The growth factor, b > 1, can be
represented as b = 1 + r where r is the
rate of increase.
 The decay factor, b < 1, can be
represented as b = 1 – r, where r is the
rate of decrease.
example: Find the percent increase
or decrease.
1) y = 2(1.3)x
b = 1.3 which is > 1 so it is an increase (exponential growth).
so b = 1 + r
1.3 = 1 + r substituting 1.3 for b
0.3 = r
subtracting 1 from both sides
So the percent of increase is 30%
2) y = 0.35(0.65)x
b = 0.65 which is < 1 so it is a decrease (exponential decay).
so b = 1 - r
0.65 = 1 - r substituting 0.65 for b
-0.35 = -r
subtracting 1 from both sides
0.35 = r
multiplying both sides by -1
So the percent of decrease is 35%
Class Work 8-1
Sketch the graph of each function.
1. y = (0.8)x
2. y = (¼ )x
Without graphing, determine whether each equation represents
exponential growth or decay.
3. y = 15(7)x
4. y = 1285(0.5)x
Write an exponential function for a graph that includes the given
points.
5. (0, 0.5), (1, 3)
6. (-1, 5), (0.5, 40)