Alg+Unit+7

=Exponential Functions= //Below are links to help better understand Geometric Sequences:// [|Geometric Sequencing] [|Review of Percents/Fractions/Decimals]

Remember, When describing a Geometric Sequence, you must identify: the Constant Multiplier: (CM) the Starting Value: f(0)

Constant Multiplier
//The constant multiplier can be found by dividing any term by it's previous term//


 * __Example:__** Find the Constant Multiplier given the sequence: 256, 179.2, 125.44, 87.808,...

Solution: 179.2 **/** 256 = **.7** ; 125.44 ** / ** 179.2 = **.7** ; 87.808 **/** 125.44 = ** .7 ** ; The constant multiplier is **.7**

//The constant multiplier can help to understand the percent increase and decrease between each number in the sequence. The constant multiplier can be broken into two different formulas. One formula is for an increasing sequence while the other is for a decreasing sequence. The formulas are listed below...//


 * Increasing Geometric Sequence: //CM = (1 + r)// where "//r//" represent the percent expressed as a decimal**


 * Decreasing Geometric Sequence: //CM = (1 - r)// where "//r//" represent the percent expressed as a decimal**

__**Example #1:**__ What is the percent increase/decrease of the given sequence: 256, 179.2, 125.44, 87.808,...

Solution: As found above, the CM is **.7**. To find the percent decrease use the formula from above to find that the percent decrease is 30%. Extra work can be seen below in the link.

What is the percent increase/decrease of the given sequence: 256, 179.2, 125.44, 87.808,... (link is being updated)

__**Example #2:**__ What is the percent increase/decrease of the given sequence: 32, 64, 128, 256,...

Solution: The CM is **1.5**. To find the percent increase, use the formula from above to find that the percent decrease is 50%. Extra work can be seen below in the link.

What is the percent increase/decrease of the given sequence: 32, 64, 128, 256,... (link is being updated)

Exponential Equations
Examples of using exponential equations

Exponential Regressions
[|How to make an exponential regression] (Go to page 5)

Extra Exponential Growth and Decay
They following notes are to help understand Exponential Growth and Decay. Examples are included.

Solving Systems with Linear and Exponential Equations
To help with solving go to the website [|www.rentcalculators.org/stheli.html] and click on the free calculator link.