Writing Exponential Equations

An exponential equation is an equation in which a variable appears in the exponent, typically in the form of y = a * b^x, where a is a constant, b is the base, and x is the exponent.

The base in an exponential equation is the number that is raised to a power. In the equation y = a * b^x, b is the base.

An exponential function is increasing if the base (b) is greater than 1, meaning as x increases, y also increases.

An exponential function is decreasing if the base (b) is between 0 and 1, meaning as x increases, y decreases.

Identify the initial value and the growth/decay factor, then use the form y = a * b^x, where a is the initial value and b is the growth/decay factor.

Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.

The general form of an exponential function is y = a * b^x, where a is the initial amount, b is the base (growth/decay factor), and x is the exponent.

The growth factor is the base (b) in the equation y = a * b^x. If b > 1, it indicates growth; if 0 < b < 1, it indicates decay.

The initial value (a) represents the starting amount before any growth or decay occurs.

To graph an exponential function, plot points for various values of x, then draw a smooth curve that approaches the x-axis but never touches it.