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Exponential & Logarithmic Models

Exponential & Logarithmic Models. 3.5. Common Models. The five most common models involving exponential and logarithmic functions are: Exponential Growth y = ae bx b>0 Exponential Decay y = ae -bx b>0 Gaussian Model Logistic Growth Logarithmic y = a + b∙ln x

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Exponential & Logarithmic Models

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  1. Exponential & Logarithmic Models 3.5

  2. Common Models The five most common models involving exponential and logarithmic functions are: Exponential Growth y = aebx b>0 Exponential Decay y = ae-bx b>0 Gaussian Model Logistic Growth Logarithmic y = a + b∙ln x y = a + b∙log10 x

  3. Exponential Growth & Decay An exponential model increases or decreases by the same percent each year. Examples include: population growth, decay of organic matter, half-life, carbon dating, and compounding interest continuously. y = ex y = e-x

  4. Gaussian Models This type of model is often used in probability and statistics to represent populations that are normally distributed. The graph is called a bell-shaped curve. The average value for a population can be found from the bell-shaped curve by observing where the maximum y-value occurs. Examples are test scores!!!

  5. Logistic Growth Some populations start out with a rapid growth followed by a declining rate of growth. Examples include bacteria growth and spread of a virus.

  6. Logarithmic Models Examples include intensity of earthquakes!!!

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