Algebra 1 CH 8.5 Write and Graph Exponential Growth Functions
Algebra 1 CH 8.5 Write and Graph Exponential Growth Functions.notebook Write and Graph Exponential Functions
Write and Graph Exponential Functions x
Objective: Write exponential functions and recognize their graphs
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y
Feb 178:53 PM
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8
x
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Feb 178:53 PM
Write and Graph Exponential Functions
Write and Graph Exponential Functions
An exponential function has the variable as the exponent.
April 30, 2015
Properties of Parent Exponential Functions
1.
The domain of each function is the set of real numbers
2.
The range of each function is the set of positive real numbers
3.
The yintercept of each graph is a.
a = initial condition (starting point)
b = growth factor with b > 1 , b can be less than one and we will see this in CH 8.6
x = the variable, frequently in word problems, it stands for time, and the variable t is frequently used.
Feb 178:53 PM
Write and Graph Exponential Functions
Feb 178:53 PM
Write and Graph Exponential Functions
Properties of Parent Exponential Functions
4.
The graph never crosses the xaxis. The parent exponential curve has no xintercepts.
5.
In one of two quadrants, the graph gets closer and closer to the xaxis, but never touches it. The xaxis is an asymptote of the graph.
Graph the function: Make a table of values: x y
Feb 178:53 PM
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2
1
0
1
2
3
1
2
4
8
Feb 178:53 PM
1
Algebra 1 CH 8.5 Write and Graph Exponential Growth Functions.notebook Write and Graph Exponential Functions
April 30, 2015
Write and Graph Exponential Functions
Graph the function: Make a table of values:
x
3
2
1
0
y
Feb 178:53 PM
1
2
3
2
8
32
Feb 178:53 PM
Write and Graph Exponential Functions
Write and Graph Exponential Functions If you are dealing with a problem where things grow in value at an annual rate, the following equation can be used.
a = initial condition (starting point)
r = annual percent increase rate
x
3
2
1
y
0
1
2
3
2
8
32
Feb 178:53 PM
Suppose you bought a house in 2005 for $120,000 and it increases in value at 4% per year. Find an equation that gives the house’s value x years after 2005.
r = 0.04
Feb 178:53 PM
t =time in years
Feb 178:53 PM
Write and Graph Exponential Functions
a = 120,000
1 + r = growth factor
Write and Graph Exponential Functions Predict the house’s value in 2013.
x = 2013 2005= 8
t =x
Feb 178:53 PM
2
Algebra 1 CH 8.5 Write and Graph Exponential Growth Functions.notebook Write and Graph Exponential Functions An antique painting is valued at $17,000 right now and it increases in value at 2.5% per year. How much will it be worth in 20 years? a = 17,000
r = 0.025
Feb 178:53 PM
t =20
April 30, 2015
Write and Graph Exponential Functions
Objective: Write exponential functions and recognize their graphs
Feb 178:53 PM
3
Write and Graph Exponential Functions x
Objective: Write exponential functions and recognize their graphs
3
2
1
y
Feb 178:53 PM
0
1
2
3
1
2
4
8
x
3
2
1
0
1
2
3
y
13
10
7
4
1
2
5
Feb 178:53 PM
Write and Graph Exponential Functions
Write and Graph Exponential Functions
An exponential function has the variable as the exponent.
April 30, 2015
Properties of Parent Exponential Functions
1.
The domain of each function is the set of real numbers
2.
The range of each function is the set of positive real numbers
3.
The yintercept of each graph is a.
a = initial condition (starting point)
b = growth factor with b > 1 , b can be less than one and we will see this in CH 8.6
x = the variable, frequently in word problems, it stands for time, and the variable t is frequently used.
Feb 178:53 PM
Write and Graph Exponential Functions
Feb 178:53 PM
Write and Graph Exponential Functions
Properties of Parent Exponential Functions
4.
The graph never crosses the xaxis. The parent exponential curve has no xintercepts.
5.
In one of two quadrants, the graph gets closer and closer to the xaxis, but never touches it. The xaxis is an asymptote of the graph.
Graph the function: Make a table of values: x y
Feb 178:53 PM
3
2
1
0
1
2
3
1
2
4
8
Feb 178:53 PM
1
Algebra 1 CH 8.5 Write and Graph Exponential Growth Functions.notebook Write and Graph Exponential Functions
April 30, 2015
Write and Graph Exponential Functions
Graph the function: Make a table of values:
x
3
2
1
0
y
Feb 178:53 PM
1
2
3
2
8
32
Feb 178:53 PM
Write and Graph Exponential Functions
Write and Graph Exponential Functions If you are dealing with a problem where things grow in value at an annual rate, the following equation can be used.
a = initial condition (starting point)
r = annual percent increase rate
x
3
2
1
y
0
1
2
3
2
8
32
Feb 178:53 PM
Suppose you bought a house in 2005 for $120,000 and it increases in value at 4% per year. Find an equation that gives the house’s value x years after 2005.
r = 0.04
Feb 178:53 PM
t =time in years
Feb 178:53 PM
Write and Graph Exponential Functions
a = 120,000
1 + r = growth factor
Write and Graph Exponential Functions Predict the house’s value in 2013.
x = 2013 2005= 8
t =x
Feb 178:53 PM
2
Algebra 1 CH 8.5 Write and Graph Exponential Growth Functions.notebook Write and Graph Exponential Functions An antique painting is valued at $17,000 right now and it increases in value at 2.5% per year. How much will it be worth in 20 years? a = 17,000
r = 0.025
Feb 178:53 PM
t =20
April 30, 2015
Write and Graph Exponential Functions
Objective: Write exponential functions and recognize their graphs
Feb 178:53 PM
3
