Flashcards: Graphing Exponential Functions — 11 cards

What is the general form of an exponential function?

$f(x)=b^x$ where b is a constant base and x is the exponent.

Exponential Function Base Label

b > 1 for growth, 0 < b < 1 for decay

What base values define exponential growth and decay functions?

Growth has base $b>1$; decay has base $0<b<1$.

Asymptote of Exponential Graph

Horizontal line y=0

What formula models exponential growth with initial amount a and rate r?

$A(t)=a(1+r)^t$ models exponential growth.

Growth Model Formula

A(t)=a(1+r)^t

What formula models exponential decay with initial amount a and decay rate r?

$A(t)=a(1-r)^t$ models exponential decay.

Decay Model Formula

A(t)=a(1-r)^t

Basic Exponential Graph Features

Domain all reals, range positive, y-intercept (0,1), asymptote y=0

Transformations Formula

$g(x)=ab^{x-h}+k$

Influence of a in Transformations

Controls vertical stretch/reflection