"Will geometric sequences be exponential functions?"
(geometric sequences whose graphs increase or decrease)
Let's compare the formulas for an geometric sequence with that of an exponential linear function.
We will be using functional notation for the sequence.
an = a1 • r(n - 1) will be written as f (n) = f (1) • r (n - 1)
Geometric Sequence:
Exponential Function: f (x) = a• bx |
Geometric Function:
n is the variable
(variable is an exponent)
r is the common ratio
f (1) is a constant.
|
Exponential Function:
x is the variable
(variable is an exponent)
b is growth/decay factor
a is a constant.
|
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Convert the Geometric Function to an Exponential Function:
Rename the "parts". (Make n = x. r = b)
f (n) = f (1) • rn - 1
f (x) = a • bx - 1 which is the same form as f (x) = a • bx
Geometric sequences whose graphs increase (or decrease) are exponential functions. |
