exponential functions 1. exponents review remember, the following basic exponent rules:

Exponential Functions

1. Exponents Review

• Remember, the following basic exponent rules:


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


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



• Ex1 (I DO): f(x) = 3x

X Y

-2 .111

-1 .333

0 1

1 3

2 9

5 243


• Called exponential function because it grows exponentially

• Output values start really small and get really big, really fast.




• 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



• 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



• Ex1 (WE DO): f(x) = 2x

X Y

-2 .250

-1 .500

0 1

1 2

2 4

5 32



• 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





• Ex2 (WE DO): f(x) = 4(1/2)x

X Y

-2 16

-1 8

0 4

1 2

2 1

5 0.125


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)


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


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


= 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%


f(x) = 4(1/2)x

X Y

-2 16

-1 8

0 4

1 2

2 1

5 0.125


= 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


6. How to find the Y-Intercept

How to find the y-intercept?

f(x) = 3x

X Y

-2 .111

-1 .333

0 1

1 3

2 9

5 243

Remember: X=0 at the y-intercept

(0,1) is the y-intercept

f(x) = 4(1/2)x

X Y

-2 16

-1 8

0 4

1 2

2 1

5 0.125

(0,4) is the y-intercept

exponential functions 1. exponents review remember, the following basic exponent rules:

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