Class
Meeting #10
The
Exponenfial
Fun+tio.n
*Pasic
furm:
y:
a'
or
(x)
= 4", tvhetre
a
)0,
a
*
1.
ais
called
the base.
Give
examples.
-The
base e
(x
2.72)
(will
discuss
a little
later)
is
used
in
continuous
growth
or
decay
models.
-tvtost
gE9ral
forq
f(*)
:
ao
,
where
u
is
a
function
of x.
(in
the
above
base fomr.
u
=
x).
.
-Non-basic
forms are formed
when
the
base a is
not
a
positive
integer
or e
OR
if the power
is
not
x.
Examples: y=(Yr).
,
y=7'*-t,
Basic
praphq
and their
prooerties
y
=
e-"
.
Show
how
to
&t
their
Saphs
on
the TI-g3.
1)
functions
are
increasing
for
all
x
2)
domains
are
all
x
3)
y
>
0
(curves
are
always
above
the
x
axis)
4)
as
x+
-oo,
f(x)-+0,
so
50
is
ahorizontal
asymptote
5)
tunctions
ay
l-1 (satisfu
the
horizontar
ri""iesif
rrri,
properfy
is
important
for
the
existence
of
their
inverses
6)
the
graphs
are
concave
up
for
all
values
in
the
a.*"i"
The
Basic
Loeerithmic
functions
-These
are the
inverses
of the
basic
orponential
lirnctions
f(x):
log ,x
is
the inverse
off(x)
=
2*
(x)
:
lOg
rox
is
the
inverse
of(x):
t0'
f(x)
:
Iog
ex is
the inverse
of(x):6*
*You
can
get
the
graphs
ofthe inverses
by
reflecting
the
original
crrrve
about
the line
y
=
x
(show
graphs)
-The
base 101og
is
called
the
cot4mon
los
and
the
10
is
usually
flot
wdtten,
(see
1og
on
your
calculator)
*The
base
e
log
is cafled
the
natural
loe
and has
a
special
symbol,
ln,
so
log.
l?
=
ln
17.
This
log
function
is
mainly used in
calculus
&
engineering
related
problems.
(u
ti*
times
in
busirrlss,
as 11/e
shall
see)
