What is the general form of an exponential function?
where b is a constant base and x is the exponent.
What base values define exponential growth and decay functions?
Growth has base ; decay has base .
What formula models exponential growth with initial amount a and rate r?
models exponential growth.
What formula models exponential decay with initial amount a and decay rate r?
models exponential decay.
Exponential Function Base Label
b > 1 for growth, 0 < b < 1 for decay
Asymptote of Exponential Graph
Horizontal line y=0
Growth Model Formula
A(t)=a(1+r)^t
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
Influence of a in Transformations
Controls vertical stretch/reflection
Answer 11 questions on Graphing Exponential Functions.
1. Which expression represents an exponential function in which the variable appears in the exponent?
2. What condition on the base indicates exponential decay for a function of the form ?
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