Extended LSAE-Exponential Functions for 3/28/25

The domain of an exponential function is all real numbers, typically expressed as (-∞, ∞).

The general form is y = a(b^x), where a is a constant, b is the base, and x is the exponent.

Exponential growth occurs when the growth rate of a value is proportional to its current value, typically represented by a function of the form y = a(b^x) where b > 1.

Exponential decay occurs when the value decreases at a rate proportional to its current value, typically represented by a function of the form y = a(b^x) where 0 < b < 1.

The y-intercept is found by evaluating the function at x = 0, which gives y = a(b^0) = a.

The range of an exponential function is (0, ∞) for growth and (0, a) for decay, where a is the initial value.

The base determines the rate of growth or decay; if b > 1, the function grows, and if 0 < b < 1, the function decays.

An exponential function will show a constant ratio between consecutive y-values when x-values are equally spaced.

The growth factor is represented by the base b in the function y = a(b^x).

Linear functions have a constant rate of change, while exponential functions have a rate of change that increases or decreases exponentially.