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**Exponential Growth and Decay Modeling**

Commonly used for the growth of population of animals, societies, and bacteria Exponential Growth and Decay Modeling Ex-Pun-Entail (Entails extreme puns) (Models were not harmed in the making of this PowerPoint)

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**Exponential Population Model**

Commonly used for the growth of population of animals, societies, and bacteria P = Population t = Time P0 = Initial Population r = Rate of growth as a decimal

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**If r > 0 then the function is exponential growth**

If r < 0 then the function is exponential decay

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**Examples of the Population Model**

If Wisconsin Rapids in 1913 had 3000 people (don’t quote me), and the population grew about 8% per year what would the population be in 2013?

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**Examples of the Population Model (cont.)**

Plug in the values into the equation Solve the equation =6,599,284 people

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Bacteria Growth Model

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**Examples of the Bacteria Growth Model**

Plaque (bacteria on the tooth) can build up on the teeth if the toothbrush or floss does not reach a certain section of the tooth. If 10 bacteria start on the tooth and doubles every hour, how much bacteria will be on the tooth in 3 days?

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**Examples of Bacteria Growth Model cont.**

10× 2 72 Plug in the equation 10× 2 72 = × 10 22 Multiply it through

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Decay Model

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**Example of The Decay Model**

A calm evacuation was announced throughout the city of Towncityville, AL. The people of the city were chosen at random to be evacuated per day. The amount of people evacuated increased by 2% per day. If the population started out as 1,000,000 people, what was the population after 6 days?

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**Example of Decay Model (cont.)**

Input the variables into the equation Solve the equation =

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“Thank You!” (Your Welcome) (Not you Chono)

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References The Official Book of the Pre-Calculus (Graphical, Numerical, Algebraic) ^Instruction^ Mrs. Peterson (French Teacher) ^Activity^ Chono ^Introduction^

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