Exponential Functions

An exponential function is a mathematical function of the form f(x) = a * b^x, where a and b are constants and b is the base of the exponent. The variable x represents the exponent, and it can take on any real value.

Key Characteristics

• Base (b): Determines the rate of growth or decay of the function.
• Exponent (x): Represents the input variable that determines the value of the function.
• Constant (a): A scaling factor that affects the vertical shift of the graph.
• Growth and Decay: Exponential functions can model either exponential growth (when b > 1) or exponential decay (when 0 < b < 1).

Graphing Exponential Functions

When graphing exponential functions, the key points to consider are the y-intercept, the direction of growth or decay, and the general shape of the graph, which tends to be a curve that either increases or decreases rapidly depending on the value of the base.

Real-Life Applications

Exponential functions are commonly used to model processes such as population growth, compound interest, radioactive decay, and the spread of diseases. They also have applications in fields such as finance, biology, physics, and computer science.