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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The five most common models involving exponential and logarithmic functions are:
Exponential Growth y = aebx b>0
Exponential Decay y = ae-bx b>0
Logarithmic y = a + b∙ln x
y = a + b∙log10 x
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
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!!!
Some populations start out with a rapid growth followed by a declining rate of growth. Examples include bacteria growth and spread of a virus.
Examples include intensity of earthquakes!!!