Growth, Decay, and Inverses

Exponential functions model rapid growth or decay, such as populations or radioactive substances. They have the form \( f(x) = a \cdot b^x \). Logarithmic functions are their inverses, answering the question: "To what power must we raise \( b \) to get \( x \)?"

Key Features

• Exponential Growth: \( b > 1 \), like money in a savings account.
• Exponential Decay: \( 0 < b < 1 \), like medicine leaving your body.
• Logarithms: Useful for solving equations where the variable is an exponent.

Applications

These functions help us understand phenomena like earthquakes, sound intensity, and viral videos going viral!