Class
Meeting
#11
Expouential
growth
& deeay
Ponulation
Models:
(simple
models)
N
=
NoeH, whereN
=
amount
pres€nt
at
anytime
t
N"
=
initial
amount
(at
t
*
0,
a constant)
k:
positive
coostant
(growth),
negative
constant
(decay)
Exanrple: If 5,000
bacterial
grow
to 8,000
in
2
hours,
how long
would ittakefor
any
starting
numberto
triple?
*Radioactive
decay
uses t}re
same
model
-Egeife!,
the time required
for
half
ofthe
zubstance
to
decompose.
(the
oonstant
k will
be
negative)
Examplej
After 500
years,
radium
226has
decayed
to8a.4a/a
ofits
original
mass.
Find
the
hatf-life.
Comoound
fnterest
-A)
Simple interest:
The
amount
deposited,
Ao,
with
interest
rate of
f/o(expressed
as a decimal),
eams rAo,
It is
usually credited
after a
given
unit
oftime
(annually-once
a
year)(semi-annuafiy-twice
a
year)
(quartedy-
four times
a
yearXdaily-365
times
a
year)(contimrously-at
each
iastant
in
time).
-B)
Cqmpound int€resL
Interest
on
principle
amount
and
previous
interest
credited.
Interest
can
be
compounded
yeady,
semi-annually
(every
6
months),
Quarterly
(overy
4
montls),
monthly
(12
times
a
yeart
daily.
or
continuously.
*Pass
out
the
handout
& briefly
discuss.
E-xample: How
many
dollars must
be invested
at
the
annual
rate
of 12Yo,
compounded
monthy,
in
order
for
the
value
ofthe iwestment
to
be
$20,000 after
5
years?.
Use
p :
po(l
+
r/n)*
