Exponential Functions

Vocabulary

asymptote

line that a graph approaches as one of the variables approaches infinity or negative infinity

base of an exponential function

value of bb in a function of the form f(x)=abxf(x)=ab^x, where aa and bb are real numbers, a0a\neq 0, b>0b>0, and b1b\ne1

compound interest

interest calculated on both the principal (the initial amount of money invested or lent) and any previously earned interest

decreasing function

function in which the yy-values decrease as the xx-values increase

exponential decay

decrease in a quantity by a constant percent rate per unit of time

exponential function

function, where aa and bb are real numbers, a0a\neq 0, b>0b>0, and b1b\ne1, written in the form:
f(x)=abxf(x)=ab^x

exponential growth

increase in a quantity by a constant percent rate per unit of time

exponential regression

mathematical process for finding the equation of an exponential function that best models a data set

exponential relationship

nonlinear relationship for which an exponential function is an appropriate model

increasing function

function in which the yy-values increase as the xx-values increase

parent function

function of a certain type that has the simplest algebraic rule

transformation

change of the graph of a function