Chapter 5

4 rules 1a log b b b log b 1 2 log b pq

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Unformatted text preview: igger
the
value
of
f(x)
approaches
 
 Theorem
:

Let
a
be
any
real
number.

The
instantaneous
rate
of
change
of
the
 function
 f ( x ) = e x at x = a is ea 


So
the
instantaneous
rate
of
change
of
the
function
 f ( x ) = e x 
at
the
point
 ( a ,e a ) is ea .

This
property
is
unique
to
the
exponential
 function
 f ( x ) = e x 
or
constant
multiples
of
the
exponential
function
such
as
 f ( x ) = ke x where k is a constant.
 
 You
will
have
to
remember
and
use
this
theorem
frequently
when
you
take
Calculus.
 
 
 
 
 
 
 
 x Ex:


In
a
biology
experiment,
let
N(t)
be
the
number
of
bacteria
in
a
colony
after
t
 hours,
where
t
=
0
corresponds
to
the
time
the
experiment
begins.

Suppose
that
 during
the
period
from
t
=
4
hours
to
t
=
8
hours
the
number
of
bacteria
is
modeled
 by
the
experimental
function
N(t)
=
4et
:
 
 
...
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This note was uploaded on 02/08/2011 for the course MATH 3 taught by Professor Staff during the Winter '08 term at UCSC.

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