Exponential Growth & Decay

function form

𝐲=𝐚(𝐛)^𝐱

𝐚=y intercept

𝐛=growth or decay factor

Arithmetic Sequence

Increase or decrease by adding/subtracting a constant (common difference) between terms, creating linear growth

Geometric Sequence

Multiply or divide by a constant (common ratio), creating exponential growth or decay because while the factor is the same, due to being a fraction or percent it will be an inconsistent numerical change in data

Growth factor

𝐛>1

Decay factor

0<𝐛<1

*Can’t have negative decay factors; it produces undefined or complex numbers for many exponents, destroying the continuous, smooth decay pattern required for modeling