This preview shows page 1. Sign up to view the full content.
Holy Cross College, Fall Semester, 2003
Math 131, Professor Hwang
Descriptions of Exponential Growth
The text has three ways of describing exponential growth.
While these three methods are
mathematically equivalent, the book’s terminology about “rate of growth/decay” can be confusing,
and demands careful attention to wording.
General Base
Let
a >
0 be a positive constant. The general exponential function with base
a
is a function of the form
f
(
t
) =
P
0
a
t
.
Usually the variable
t
represents time, measured in units appropriate to a given problem.
The
constant
P
0
represents the amount of “stuF” at time 0.
±or each increment of
t
by one unit, an exponential function’s value gets multiplied by
a
, because
f
(
t
+ 1) =
P
0
a
t
+1
=
P
0
a
t
·
a
=
a
·
f
(
t
)
.
Consequently, if 0
< a <
1, then
f
is decreasing (by a factor of
a
for each time unit), while if
a >
1,
then
f
is increasing (by a factor of
a
for each time step).
Growth Rate
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 03/26/2012 for the course MAC 2312 taught by Professor Bonner during the Fall '08 term at University of Florida.
 Fall '08
 Bonner
 Math, Calculus

Click to edit the document details