3.5

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

cbxaey2

rxbe

ay 1

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!!!