1. 7.1 & 7.2 - Graphing Exponential Transformations
Do NOW
Exponential Equation: f(x) = Cax
C: COEFFICIENT
a: BASE
X: EXPONENT
Exponential Equations
Graph is above the x-axis
Domain: (–∞, ∞); Range: (0, ∞)
Exponential Growth
When the base is greater than 1, a > 1
f(x) is INCREASING
Exponential Decay
When the base is between zero and one, 0 < a < 1
f(x) is DECREASING
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7.1 & Graphing Exponential Transformations

2. 7.1 & 7.2 - Graphing Exponential Transformations
Worksheet Key
Exponential Equation: f(x) = Cax
C: COEFFICIENT
a: BASE
X: EXPONENT
Exponential Equations
Graph is above the x-axis
Domain: (–∞, ∞); Range: (0, ∞)
Exponential Growth
When the base is greater than 1, a > 1
f(x) is INCREASING
Exponential Decay
When the base is between zero and one, 0 < a < 1
f(x) is DECREASING
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7.1 & Graphing Exponential Transformations

3. Graphing Exponential Functions
Section 7.1 and 7.2,
Revised ©2013,
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7.1 & Graphing Exponential Transformations

4. 7.1 & 7.2 - Graphing Exponential Transformations
Review
Linear
Quadratic
Algebraically
Equation: 9x + 3y = –6
Equation: y = 5x2 – 7x + 3
Verbally
Line
Parabola
Table
Common Difference
Common Ratio
Graph x 1 2 3 y 4 9 x 1 2 3 y 16 8 4
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7.1 & Graphing Exponential Transformations

5. Growth vs Decay Algebraically Verbally Table Graph
Exp. Growth
Exp. Decay
Algebraically
Verbally
Increases by the same rate in each time period
Examples: Population, Compound Interest, Cell Growth, and Bacteria
Decreases by the same rate in each time period
Examples: Investment Loss, Evaporation, Depreciation
Table
X increases, Y increases
X increases, Y decreases
Graph
Algebraically
Equation:
y = c • (1 + r)x
c: Initial Value
r: Percentage
x: Time Period
y = c • (1 – r)x x 1 2 3 y 4 8 16 x 1 2 3 y 16 8 4
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7.1 & Graphing Exponential Transformations

6. 7.1 & 7.2 - Graphing Exponential Transformations
Example 1
Determine whether represents exponential growth or decay.
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7.1 & Graphing Exponential Transformations

7. 7.1 & 7.2 - Graphing Exponential Transformations
Example 2
Determine whether represents exponential growth or decay.
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7.1 & Graphing Exponential Transformations

8. 7.1 & 7.2 - Graphing Exponential Transformations
Your Turn
Determine whether represents exponential growth or decay.
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7.1 & Graphing Exponential Transformations

9. Graphing Exponentials
Make a table of values, usually from [–3, 3]
Plot the points from the table
Connect the dots and draw from left to right, a smooth curve and label any asymptotes
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7.1 & Graphing Exponential Transformations

10. 7.1 & 7.2 - Graphing Exponential Transformations
Example 3
Graph f(x) = 2x x
f(x) –3
(2)–3
1/8 –2
(2)–2
1/4 –1
(2)–1
1/2
(2)0 1
(2)1 2
(2)2 4 3
(2)3 8 x
f(x) –3
(2)–3 –2
(2)–2 –1
(2)–1
(2)0 1
(2)1 2
(2)2 3
(2)3 x
f(x) –3 –2 –1 1 2 3
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7.1 & Graphing Exponential Transformations

11. 7.1 & 7.2 - Graphing Exponential Transformations
Example 3
Graph f(x) = 2x x
f(x) –3
(2)–3
1/8 –2
(2)–2
1/4 –1
(2)–1
1/2
(2)0 1
(2)1 2
(2)2 4 3
(2)3 8
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7.1 & Graphing Exponential Transformations

12. 7.1 & 7.2 - Graphing Exponential Transformations
Example 3
Graph f(x) = 2x (Calculator check)
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7.1 & Graphing Exponential Transformations

13. 7.1 & 7.2 - Graphing Exponential Transformations
Example 4
Graph f(x) = (1/2)x x
f(x) –3
(1/2)–3 8 –2
(1/2)–2 4 –1
(1/2)–1 2
(1/2)0 1
(1/2)1
1/2
(1/2)2
1/4 3
(1/2)3
1/8 x
f(x) –3
(1/2)–3 –2
(1/2)–2 –1
(1/2)–1
(1/2)0 1
(1/2)1 2
(1/2)2 3
(1/2)3 x
f(x) –3 –2 –1 1 2 3
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7.1 & Graphing Exponential Transformations

14. 7.1 & 7.2 - Graphing Exponential Transformations
Example 4
Graph f(x) = (1/2)x x
f(x) –3
(1/2)–3 8 –2
(1/2)–2 4 –1
(1/2)–1 2
(1/2)0 1
(1/2)1
1/2
(1/2)2
1/4 3
(1/2)3
1/8
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7.1 & Graphing Exponential Transformations

15. 7.1 & 7.2 - Graphing Exponential Transformations
Example 5
Graph f(x) = 3(2/3)x (decimals are acceptable) x
f(x) –3 –2 –1 1 2 3 –3
3(2/3)–3
10.125 –2
3(2/3)–2
6.75 –1
3(2/3)–1
4.5
3(2/3)0 3 1
3(2/3)1 2
3(2/3)2
5/3
3(2/3)3
.889
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7.1 & Graphing Exponential Transformations

16. 7.1 & 7.2 - Graphing Exponential Transformations
Your Turn
Graph f(x) = 1/2(2)x (decimals are acceptable) x
f(x) –3 –2 –1 1 2 3 –3
1/2(2)–3
0.0625 –2
1/2(2)–2
.125 –1
1/2(2)–1
.25
1/2(2)0
0.5 1
1/2(2)1 2
1/2(2)2 3
1/2(2)3 4
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7.1 & Graphing Exponential Transformations

17. Exponential Growth/Decay Formula
Equation, y = a(1 + r)t
a = Initial Amount
r = Interest Rate
+ = Growth/Decay Rate
t = time
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7.1 & Graphing Exponential Transformations

18. 7.1 & 7.2 - Graphing Exponential Transformations
Example 6
The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. Write a function that models the value of the car over time. Then, determine the value of the car in 2004.
C = ??
A = 11,000
R = 0.069
T = t
C =
A =
R =
T =
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7.1 & Graphing Exponential Transformations

19. 7.1 & 7.2 - Graphing Exponential Transformations
Example 6
The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. Write a function that models the value of the car over time. Then, determine the value of the car in 2004.
C = ??
A = 11,000
R = 0.069
T = 20
C =
A =
R =
T =
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7.1 & Graphing Exponential Transformations

20. 7.1 & 7.2 - Graphing Exponential Transformations
Example 7
You put $350 into a savings account that earns 3% annual interest compounded yearly. How much will your investment be worth in 4 years?
C = ??
A = 350
R = 0.03
T = 4
C =
A =
R =
T =
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7.1 & Graphing Exponential Transformations

21. 7.1 & 7.2 - Graphing Exponential Transformations
Your Turn
The owner of an original copy of a 1938 comic book sold it at an auction in The owner bought the comic book for $55 in The value of the comic book increased at a rate of 2.8% per year. Write a function and determine the approximate value in 2008.
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7.1 & Graphing Exponential Transformations

22. 7.1 & 7.2 - Graphing Exponential Transformations
Assignment
Worksheet
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7.1 & Graphing Exponential Transformations