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
Exponential & Logarithmic Models
The five most common models involving exponential and logarithmic functions are:
Exponential Growthy = aebx b>0
Exponential Decayy = ae-bx b>0
Logarithmicy = 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 = exy = 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!!!