exponential & logarithmic models
DESCRIPTION
Exponential & Logarithmic Models. 3.5. Common Models. The five most common models involving exponential and logarithmic functions are: Exponential Growthy = ae bx b>0 Exponential Decayy = ae -bx b>0 Gaussian Model Logistic Growth Logarithmicy = a + b∙ln x - PowerPoint PPT PresentationTRANSCRIPT
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3.5
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The five most common models involving exponential and logarithmic functions are:
1.Exponential Growth y = aebx b>0
2.Exponential Decay y = ae-bx b>0
3.Gaussian Model
4.Logistic Growth
5.Logarithmic y = a + b∙ln xy = a + b∙log10 x
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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
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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!!!
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Some populations start out with a rapid growth followed by a declining rate of growth. Examples include bacteria growth and spread of a virus.
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Examples include intensity of earthquakes!!!