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2 ALI
S
HA
B
E
R
KAUZE
R
T
A
B
LE O
F
CONTENT
S
P
rob
l
e
m
St
a
t
e
m
en
t
................................................................................................................... 3
M
o
ti
va
ti
on ................................................................................................................................... 4
M
a
t
he
m
a
ti
ca
l
De
s
cr
i
p
ti
on and
S
o
l
u
ti
on Approach .................................................... 4
D
is
cu
ssi
on ................................................................................................................................... 7
C
onc
l
u
si
on and
R
eco
mm
enda
ti
on
s
................................................................................... 8
No
m
enc
l
a
t
ure ............................................................................................................................. 9
R
eference ................................................................................................................................... 10
Berkauzer: The Effects of Age on Short-Term Memory Loss due to Proactive Int
Produced by The Berkeley Electronic Press, 2011
AGE AND
P
R
OA
C
TIVE
S
HO
R
T TE
R
M
M
E
M
O
R
Y LO
SS
3
P
R
O
B
LE
M
STATE
M
ENT
The goa
l
of
t
h
i
s
pro
j
ec
t
is
t
o de
t
er
mi
ne
t
he op
tim
a
l
age for re
t
a
i
n
i
ng o
l
d
i
nfor
m
a
ti
on a
s
new
i
nfor
m
a
ti
on
is
i
n
t
roduced crea
ti
ng proac
ti
ve
i
n
t
erference.
Si
x peop
l
e fro
m
age
s
f
i
f
t
een
t
o
for
t
y were
t
e
st
ed
i
nd
i
v
i
dua
ll
y u
si
ng a
s
e
t
co
l
or pa
tt
ern and each per
s
on wa
s
a
ssi
gned a pa
tt
ern
d
i
ff
i
cu
lt
y
l
eve
l
(
P
DL) rang
i
ng fro
m
one
t
o n
i
ne.
The
P
DL repre
s
en
ts
t
he h
i
ghe
st
co
m
b
i
na
ti
on of co
l
or
s
t
he per
s
on cou
l
d re
m
e
m
ber
w
it
hou
t
any error when repea
ti
ng
t
he
m
.
F
ro
m
t
h
is
i
nfor
m
a
ti
on,
t
he pa
tt
ern d
i
ff
i
cu
lt
y
l
eve
l
wa
s
p
l
o
tt
ed aga
i
n
st
t
he
i
nd
i
v
i
dua
l
'
s
age and f
itt
ed by po
l
yno
mi
a
l
regre
ssi
on.
B
a
s
ed on our re
s
u
lts
,
t
he
peak age (op
tim
a
l
age) for re
m
e
m
ber
i
ng o
l
d
i
nfor
m
a
ti
on when new
i
nfor
m
a
ti
on
is
pre
s
en
t
ed,
is
t
wen
t
y four. A
lt
hough
t
he re
s
u
lts
were no
t
a perfec
t
-
m
a
t
ch w
it
h
t
he o
t
her
st
ud
i
e
s
, wh
i
ch
s
how
t
ha
t
t
he peak age for
m
e
m
or
i
za
ti
on
is
t
wen
t
y-
t
wo,
t
h
is
st
udy
is
con
sist
en
t
w
it
h o
t
her
st
ud
i
e
s
by
s
how
i
ng
t
ha
t
a
s
age
i
ncrea
s
e
s
,
m
e
m
ory perfor
m
ance decrea
s
e
s
. W
it
h
s
o
m
e
im
prove
m
en
ts
,
it
is
be
li
eved
t
ha
t
t
h
is
st
udy wou
l
d be
i
n co
m
p
li
ance w
it
h o
t
her we
ll
-known
st
ud
i
e
s
s
uch a
s
t
ho
s
e
conduc
t
ed by
S
a
lt
hou
s
e
C
ogn
iti
ve Ag
i
ng Lab (
S
a
lt
hou
s
e 2009) a
t
t
he Un
i
ver
sit
y of V
i
rg
i
n
i
a.
MOTIVATION
Quan
ti
fy
i
ng
t
he effec
ts
of age on
m
e
m
ory
is
si
gn
i
f
i
can
t
t
o
m
any area
s
of
st
ud
i
e
s
t
oday,
e
s
pec
i
a
ll
y
t
o
t
ho
s
e who are
i
n
t
he
m
ed
i
ca
l
f
i
e
l
d, cogn
iti
ve
st
ud
i
e
s
, and neuro
l
og
i
ca
l
st
ud
i
e
s
. A
s
t
echno
l
ogy
i
ncrea
s
e
s
,
t
he a
m
oun
t
of da
il
y
i
nfor
m
a
ti
on a per
s
on encoun
t
er
s
i
ncrea
s
e
s
a
s
we
ll
.
P
eop
l
e are con
st
an
tl
y be
i
ng expec
t
ed
t
o re
m
e
m
ber o
l
d
i
nfor
m
a
ti
on, a
s
we
ll
a
s
new
i
nfor
m
a
ti
on
pre
s
en
t
ed
t
o
t
he
m
i
n
s
hor
t
per
i
od
s
of
tim
e.
St
uden
ts
e
s
pec
i
a
ll
y are
s
ub
j
ec
t
t
o proac
ti
ve
i
n
t
erference
t
hroughou
t
t
he
i
r
st
ud
i
e
s
.
Undergraduate Journal of Mathematical Modeling: One + Two, Vol. 4, Iss. 1 [2011], Art. 2
https://digitalcommons.usf.edu/ujmm/vol4/iss1/2
DOI: http://dx.doi.org/10.5038/2326-3652.4.1.2
4 ALI
S
HA
B
E
R
KAUZE
R
P
roac
ti
ve
m
e
m
ory
st
ud
i
e
s
can be u
s
ed
t
o
m
on
it
or
t
he change
s
i
n a hea
lt
hy bra
i
n or a
ssist
i
n de
t
er
mi
n
i
ng
t
he pa
t
ho
l
ogy of var
i
ou
s
neuro
l
og
i
ca
l
d
is
order
s
s
uch a
s
de
m
en
ti
a. A
lt
hough
t
h
is
is
a ba
si
c
st
udy of
s
hor
t
-
t
er
m
m
e
m
ory
l
o
ss
,
it
can be rev
is
ed
t
o
t
e
st
o
t
her for
ms
of
m
e
m
ory
l
o
ss
.
MATHE
M
ATI
C
AL
D
E
SCR
I
P
TION AND SOLUTION
A
PPR
OA
C
H
Th
is
prob
l
e
m
requ
i
re
s
t
he
t
e
sti
ng of peop
l
e fro
m
d
i
fferen
t
age group
s
. We ob
t
a
i
ned our
da
t
a by
t
e
sti
ng
s
even peop
l
e w
it
h d
i
fferen
t
age
s
. A
s
can be
s
een by
Fi
gure 1,
t
he
P
DL
s
core
s
t
ended
t
o decrea
s
e a
s
age
i
ncrea
s
ed. Th
is
s
ugge
sts
t
ha
t
peop
l
e of grea
t
er age are w
ill
have grea
t
er
d
i
ff
i
cu
lt
y w
it
h proac
ti
ve
i
n
t
erference co
l
or pa
tt
ern
s
.
We beg
i
n by
m
ode
li
ng our da
t
a u
si
ng Exce
l
and po
l
yno
mi
a
l
regre
ssi
on.
P
o
l
yno
mi
a
l
regre
ssi
on e
st
ab
lis
he
s
a re
l
a
ti
on
s
h
i
p be
t
ween an
i
ndependen
t
var
i
ab
l
e and a dependen
t
var
i
ab
l
e
i
n
t
he for
m
of an order po
l
yno
mi
a
l
,
(1)
The coeff
i
c
i
en
ts
are e
stim
a
t
ed u
si
ng
t
he
l
ea
st
s
quare
m
e
t
hod, a nu
m
er
i
ca
l
m
e
t
hod wh
i
ch
mi
n
imi
ze
s
t
he
s
u
m
of
t
he
s
quare error
s
be
t
ween
t
he ac
t
ua
l
da
t
a po
i
n
ts
and
t
he f
itt
ed
li
ne.
A
s
can be
s
een
i
n
Fi
gure 1,
t
he exper
im
en
t
a
l
da
t
a
is
n
i
ce
l
y f
it
by
t
he 2 order (quadra
ti
c)
po
l
yno
mi
a
l
,
. (2)
Berkauzer: The Effects of Age on Short-Term Memory Loss due to Proactive Int
Produced by The Berkeley Electronic Press, 2011
AGE AND
P
R
OA
C
TIVE
S
HO
R
T TE
RM
M
E
M
O
R
Y LO
SS
5
Age
Patter
n
D
i
ff
i
c
ul
ty
L
eve
l
15 8
18 7
21 8
24 8
29 8
37 7
40 4
F
i
g
u
re 1
:
Nu
m
ber of co
l
or
s
re
m
e
m
bered
i
n
t
he pa
tt
ern
The quadra
ti
c regre
ssi
on curve (2)
s
ugge
sts
t
ha
t
, af
t
er
s
o
m
e po
i
n
t
,
s
hor
t
-
t
er
m
m
e
m
ory regre
ss
e
s
a
s
age
i
ncrea
s
e
s
. We f
i
nd
t
h
is
po
i
n
t
by
l
oca
ti
ng
t
he age where
t
he
P
DL
is
m
ax
imi
zed,
i
.e., we
f
i
nd
t
he f
i
r
st
der
i
va
ti
ve of
t
he f
itt
ed
li
ne (2) and
s
e
tti
ng
it
equa
l
t
o zero. The
m
ax
im
u
m
or peak
age of
s
hor
t
-
t
er
m
m
e
m
or
i
za
ti
on
is
reached when
. (3)
Th
is
occur
s
a
t
. Thu
s
our exper
im
en
t
a
l
da
t
a
s
how
s
t
ha
t
t
he approx
im
a
t
e peak age for
re
t
a
i
n
i
ng
s
hor
t
-
t
er
m
i
nfor
m
a
ti
on
is
24.
A
lt
hough
t
he
m
ax
im
u
m
of our regre
ssi
on func
ti
on wa
s
ea
s
y
t
o f
i
nd exp
li
c
itl
y,
t
here
is
a
po
ssi
b
ilit
y
t
ha
t
t
he f
itt
ed po
l
yno
mi
a
l
regre
ssi
on curve
is
a h
i
gher degree po
l
yno
mi
a
l
.
F
or any
po
l
yno
mi
a
l
w
it
h degree grea
t
er
t
han or equa
l
t
o ,
t
he re
s
u
lti
ng der
i
va
ti
ve beco
m
e
s
a po
l
yno
mi
a
l
of degree or grea
t
er.
F
or
s
uch ca
s
e
s
,
s
o
l
v
i
ng for
t
he zero
s
of
t
he der
i
va
ti
ve requ
i
re
s
add
iti
ona
l
co
m
pu
t
a
ti
on.
f
(x)
0
1
2
3
4
5
6
7
8
9
10
10 15 20 25 30 35 40 45
Patter
n
D
i
ff
i
c
ul
ty
L
eve
l
Age (Year
s
)
Undergraduate Journal of Mathematical Modeling: One + Two, Vol. 4, Iss. 1 [2011], Art. 2
https://digitalcommons.usf.edu/ujmm/vol4/iss1/2
DOI: http://dx.doi.org/10.5038/2326-3652.4.1.2
6 ALI
S
HA
B
E
R
KAUZE
R
D
I
SC
U
SS
ION
In
t
h
is
exper
im
en
t
,
s
even par
ti
c
i
pan
ts
fro
m
var
i
ou
s
age group
s
(15 40 year
s
o
l
d) were
g
i
ven a
s
e
t
of four co
l
ored card
s:
b
l
ue, red, orange, and
ye
ll
ow. A
t
t
he beg
i
nn
i
ng of each round, a par
ti
c
i
pan
t
wa
s
s
hown a co
l
ored card and a
s
ked
t
o reca
ll
t
he fu
ll
s
equence of
co
l
or
s
up
t
o
t
he curren
t
round.
F
our ou
t
of
t
he
s
even par
ti
c
i
pan
ts
co
m
p
l
e
t
ed round 8
w
it
hou
t
a
mist
ake. A
s
s
een
i
n Tab
l
e 1, a
ll
m
e
m
ber
s
of
t
he age
group 15 29 co
m
p
l
e
t
ed round 8 w
it
h
t
he excep
ti
on of
t
he 18
year o
l
d who co
m
p
l
e
t
ed round 7. The 40 year o
l
d par
ti
c
i
pan
t
on
l
y co
m
p
l
e
t
ed round 4, wh
i
ch
is
a very
si
gn
i
f
i
can
t
d
i
fference
co
m
pared w
it
h
t
he o
t
her
s
t
e
st
ed.
Th
is
s
ugge
sts
t
ha
t
young adu
lts
and ado
l
e
s
cen
ts
m
ay
have be
tt
er
s
hor
t
-
t
er
m
m
e
m
or
i
za
ti
on
s
k
ills
when
it
co
m
e
s
t
o
st
or
i
ng o
l
d
i
nfor
m
a
ti
on a
s
new
i
nfor
m
a
ti
on
is
added (proac
ti
ve
i
n
t
erference). The be
st
f
it
curve (2) for our da
t
a,
i
nd
i
ca
t
e
s
t
ha
t
t
he pa
tt
ern d
i
ff
i
cu
lt
y
l
eve
ls
decrea
s
e w
it
h age. The
s
e re
s
u
lts
co
m
p
l
y w
it
h a
m
ed
i
ca
l
st
udy done
by
S
a
lt
hou
s
e
t
ha
t
found
t
ha
t
t
he peak age for
st
or
i
ng
i
nfor
m
a
ti
on
is
t
wen
t
y-
t
wo (
S
a
lt
hou
s
e 2009).
CON
C
LU
S
ION AND RE
C
O
MM
ENDATION
S
B
y u
si
ng ca
l
cu
l
u
s
w
it
h
t
he a
ssist
ance of Exce
l
,
t
he peak age for
st
or
i
ng
i
nfor
m
a
ti
on wa
s
de
t
er
mi
ned
t
o be 24 year
s
o
l
d. Th
is
is
con
sist
en
t
w
it
h
t
he 2000 par
ti
c
i
pan
t
st
udy where
t
he peak
age wa
s
found
t
o be 22 (
S
a
lt
hou
s
e 2009). In fac
t
,
t
here
is
on
l
y a
sm
a
ll
percen
t
error of 9%
Ro
und
Co
l
or
1.
Bl
ue
2.
R
ed
3.
Bl
ue
4. Orange
5. Ye
ll
ow
6. Ye
ll
ow
7.
R
ed
8. Orange
9.
Bl
ue
10. Ye
ll
ow
T
a
bl
e 2:
S
equence of co
l
or
s
each par
ti
c
i
pan
t
wa
s
a
s
ked
t
o
re
m
e
m
ber.
Berkauzer: The Effects of Age on Short-Term Memory Loss due to Proactive Int
Produced by The Berkeley Electronic Press, 2011
AGE AND
P
R
OA
C
TIVE
S
HO
R
T TE
RM
M
E
M
O
R
Y LO
SS
7
be
t
ween
t
he
s
e
t
wo age
s
. Th
is
s
how
s
t
ha
t
a
l
arge-
s
ca
l
e
st
udy
is
no
t
a
l
way
s
needed
t
o f
i
nd prec
is
e
re
s
u
lts
.
I
t
s
hou
l
d be no
t
ed
t
ha
t
t
he
S
a
lt
hou
s
e
st
udy d
i
d no
t
f
i
nd
t
he decrea
s
e
i
n perfor
m
ance
t
o be
quadra
ti
c, bu
t
t
he genera
l
t
rend
s
of
t
he
t
wo
st
ud
i
e
s
are
i
n co
m
p
li
ance w
it
h one ano
t
her.
Si
nce
t
h
is
st
udy wa
s
ab
l
e
t
o conf
i
r
m
t
he f
i
nd
i
ng
s
of a
m
uch
l
arger
st
udy, we have
s
hown
t
ha
t
t
he
s
e are
prec
is
e re
s
u
lts
.
One reco
mm
enda
ti
on
is
t
o adap
t
t
he
t
e
st
t
o f
i
nd
m
ore
t
han
t
he peak age for
st
or
i
ng
i
nfor
m
a
ti
on. I
t
wou
l
d be u
s
efu
l
t
o
s
ee wha
t
t
ype of
i
nfor
m
a
ti
on
is
ea
si
er
t
o
st
ore.
F
or
s
o
m
e,
t
he
v
is
ua
l
a
s
pec
t
of
t
h
is
st
udy
m
ay have benef
it
ed
t
he
m
m
ore, bu
t
o
t
her
s
m
ay be ab
l
e
t
o re
m
e
m
ber a
s
er
i
e
s
of
s
ound
s
m
ore ea
sil
y.
M
o
st
st
ud
i
e
s
i
gnore
t
h
is
and focu
s
on
t
he v
is
ua
l
a
s
pec
ts
of re
t
a
i
n
i
ng
i
nfor
m
a
ti
on.
F
or fur
t
her
st
udy
i
ng
it
m
ay be benef
i
c
i
a
l
t
o have one
t
e
st
focu
s
on v
is
ua
l
m
e
m
ory
wh
il
e ano
t
her
t
e
sts
aud
it
ory
m
e
m
ory.
Si
nce
m
o
st
st
ud
i
e
s
s
how
t
ha
t
t
he peak age for re
t
a
i
n
i
ng
i
nfor
m
a
ti
on
is
i
n
t
he ear
l
y
t
wen
ti
e
s
, ano
t
her
st
udy cou
l
d focu
s
on a
l
arger
s
ca
l
e of peop
l
e fro
m
age 20
t
o 29
t
o be
tt
er
de
t
er
mi
ne
t
he peak age ra
t
her
t
han
s
a
m
p
li
ng o
l
der age
s
wh
i
ch have been found
t
o be beyond
peak.
B
y focu
si
ng on
t
h
is
i
n
t
erva
l
it
m
ay be ea
si
er
t
o p
i
npo
i
n
t
an exac
t
age a
t
wh
i
ch
s
hor
t
-
t
er
m
m
e
m
ory
is
be
st
re
t
a
i
ned.
Undergraduate Journal of Mathematical Modeling: One + Two, Vol. 4, Iss. 1 [2011], Art. 2
https://digitalcommons.usf.edu/ujmm/vol4/iss1/2
DOI: http://dx.doi.org/10.5038/2326-3652.4.1.2
8 ALI
S
HA
B
E
R
KAUZE
R
N
O
M
EN
C
LATU
R
E
S
ym
b
o
l
Def
ini
t
i
o
n
U
ni
t
s
Age Year
s
P
a
tt
ern d
i
ff
i
cu
lt
y
l
eve
l
C
o
l
or
C
o
m
b
i
na
ti
on
s
RE
F
E
R
EN
C
E
S
a
lt
hou
s
e, T
im
o
t
hy A. -
N
eu
r
ob
i
o
l
ogy o
f
Ag
i
ng. 30 (4)
(2009). pp. 507-514.
Berkauzer: The Effects of Age on Short-Term Memory Loss due to Proactive Int
Produced by The Berkeley Electronic Press, 2011
