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Exponential Functions
2. Exponential Functions
Non-Linear
• Exponential Functions are functions where the variable is the exponent.
• Switched from quadratic
• Examples: f(x) = 3x
P(r) = 2000(1.05)r
f(x) = 4( ½ )x
Exponential Functions
3. Graphing Exponential Functions
• Ex1 (I DO): f(x) = 3x
X Y
-2 3(-2) = 1/(32) = .111
-1 3(-1) = 1/(31) = .333
0 3(0) = 1
1 3(1) = 3
2 3(2) = 9
5 3(5) = 243
Find these two first
When x=0, y coord. is y-intercept
• Plot at least 5 points to get a good sense of the function.
• You may want to space your x values out to see growth
• 3 decimal places
Exponential Functions
3. Graphing Exponential Functions
• Ex1 (I DO): f(x) = 3x
X Y
-2 .111
-1 .333
0 1
1 3
2 9
5 243
Exponential Functions
• Called exponential function because it grows exponentially
• Output values start really small and get really big, really fast.
3. Graphing Exponential Functions
Exponential Functions
3. Graphing Exponential Functions
• Ex2 (WE DO): f(x) = 2x
X Y
-2 2(-2) = 1/(22) = .250
-1 2(-1) = 1/(21) = .500
0 2(0) = 1
1 2(1) = 2
2 2(2) = 4
5 2(5) = 32
Find these two first
When x=0, y coord. is y-intercept
• Plot at least 5 points to get a good sense of the function.
• You may want to space your x values out to see growth
• 3 decimal places
Exponential Functions
3. Graphing Exponential Functions
• Ex1 (WE DO): f(x) = 2x
X Y
-2 .250
-1 .500
0 1
1 2
2 4
5 32
Exponential Functions
3. Graphing Exponential Functions
• Ex2 (WE DO): f(x) = 4(1/2)x
X Y
-2 4(0.5)(-2) = 4/(0.52) = 16
-1 4(0.5)(-1) = 4/(0.51) = 8
0 4(0.5)(0) = 4(1) = 4
1 4(0.5)(1) = 4(0.5) = 2
2 4(0.5)(2) = 4(0.25) = 1
5 4(0.5)(5) = 4(0.0313) = 0.125
Find these two first
When x=0, y coord. is y-intercept
Exponential Functions
3. Graphing Exponential Functions
• Ex2 (WE DO): f(x) = 4(1/2)x
X Y
-2 16
-1 8
0 4
1 2
2 1
5 0.125
Exponential Functions
4. Linear vs. Exponential Growth
Linear Exponential
X Y
1 2
2 4
3 6
4 8
5 10
f(x) = 2x f(x) = 2x
+2
+2
+2
+2
X Y
1 2
2 4
3 8
4 16
5 32
times 2
times 2
times 2
times 2
Constant Rate
Add/Subtract the same value to
increase output
Constant Growth Rate
Multiply by the same value to increase output
(sometimes written as % change)
Exponential Functions
4. Linear vs. Exponential Growth
Linear Exponential• Always stated in units
(NOT percent)
• Increase/Decrease is because of adding or subtracting (NOT multiplying)
Which rate of change is it: linear or exponential?
• Always stated in percent or multiplication factor (NOT units)
• Increase/Decrease is because of multiplying (NOT adding)
a) The fish in the sea are decreasing by 10% every year
b) Mr. Vasu’s bank account increases by $3,000 every month
Exponential: 10% change
Linear: $3,000 change
Exponential Functions
5. How to find the Constant Multiplication Factor
To find the constant mult. factor
f(x) = 3x
X Y
-2 .111
-1 .333
0 1
1 3
2 9
5 243
Constant Growth Rate
= y2
y1
0.333
0.111=3
1
0.333=3
9
3=3
243
9=27
Must be consecutive ordered pairs
3.00 = 300%
Exponential Functions
f(x) = 4(1/2)x
X Y
-2 16
-1 8
0 4
1 2
2 1
5 0.125
Constant Growth Rate
= y2
y1
8
16=0.5
4
8=0.5
2
4=0.5
0.50 = 50%
To find the constant mult. factor5. How to find the Constant Multiplication Factor