1. Exponential Equations
Objective: Students will be able to write and interpret exponential equations.

2. Exponential Equations
Growth and Decay Graph grows or declines quicker than just a square, cubed, or line Looking at percentage growth and decay
a is y intercept, when x =0
b is what is being repeatedly multiplied
b>1 growth
b<1 decay

3. Growth a variables mean the same thing
r is the percent that you are increasing by (write as a decimal), such as a population
(1+r) is the b value

4. Graph of Growth
Goes up from left to right, curves up quicker than a line
When sketching growth
Make sure a is clearly marked
Plot 1 or 2 more points
Connect with a curved line

5. Decay
Similar to growth except you subtract r because your population is going down
(1-r) is the b value

6. Graph of Decay
Goes down from left to right, curves down quicker than a line, gets close to zero but never touches it
When sketching growth
Make sure a is clearly marked
Plot 1 or 2 more points
Connect with a curved line

7. Finding from a table
Look for when x = 0 this will give you the a value
Look for pattern in the y values, always multiplication, division is just multiplication of a fraction

8. Example X Y 2 1 6 18 3 54 X=0 y is 2 this is the a value2 1 6 18 3 54
X=0 y is 2 this is the a value
Constantly multiply by 3

9. Example X Y 4 1 2 3
A=4
B=1/2

10. Word Problem Growth because of word grow 1.75% Initial amount is $100
Y=100( )^X

11. Worksheet
First 2 pages give similar explanations and examples Pg 6 gives equation and examples of graphs problem 1 and 2 write what a and b are and sketch a graph and identify if growth or decay Pg 7 talks more about percentage growth and decay equations, more word problem exampes, you can use a calculator to get answers Page 3 looks at tables, graphs and equations Page 4 determine growth or decay and sketch a graph