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

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

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

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

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

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

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

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

Example X Y 4 1 2 3 ½ ¼ A=4 B=1/2

Word Problem Growth because of word grow 1.75% Initial amount is $100 Y=100(1+.0175)^X

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