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# Exponential & Logarithmic Models PowerPoint PPT Presentation

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

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## Exponential & Logarithmic Models

3.5

### Common Models

The five most common models involving exponential and logarithmic functions are:

Exponential Growthy = aebx b>0

Exponential Decayy = ae-bx b>0

Gaussian Model

Logistic Growth

Logarithmicy = a + b∙ln x

y = a + b∙log10 x

### 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 = exy = e-x

### 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!!!

### 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.

### Logarithmic Models

Examples include intensity of earthquakes!!!