PLEASE TURN OVER
Lab Section 03
MATHEMATICS MATH*1080
Lab Quiz #2
Y
SOLUTIONS YELLOW
NO CALCULATORS ALLOWED
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Initials:________
Lab Section #:______
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Student #:
Class Section #: ______
1.
Each year a bank deducts $30 as service charges on each deposit account, and then pays 10% interest on the
remaining money.
Let
denote the amount of money in a specific account at the end of year n.
\
8
(a)
Write a difference equation satisfied by the sequence {
}.
\
8
Solution
2
\
œ \
$! !Þ"Ð\
$!Ñ
Ê
\
œ \
$! !Þ"\
$
8
8
8
8
8
8
+1
+1
Ê \
œ "Þ"\
$$
8
8
+1
4
Answer (a)
\
œ "Þ"\
$$
8
8
+1
(b)
Write an expression giving the balance of the account at the end of year
if the initial deposit
is
8
\
!
$5,000.
Solution
where
, and
\
œ
\
+
+ œ "Þ"ß
, œ $$
,
,
" +
" +
8
!
8
Œ
\
œ &!!!
!
2
\
œ
&!!!
Ð"Þ"Ñ
Ê \
œ $$! %'(!Ð"Þ"Ñ
Ð$$Ñ
Ð$$Ñ
" "Þ"
" "Þ"
8
8
8
8
Œ
Answer (b)
\
œ $$! %'(!Ð"Þ"Ñ
8
8
2.
Deternine the strictly positive equilibriums for the difference equation
2
=
(
) ( 3
) are
1
6
\
\
"
\
8"
$
8
8
2
SOLUTION
=
(
) (
=
(
) (
1
1
\
\
"$ \
Ñ Ê \
\
"$ \
Ñ
8"
$'
$'
8
8
I
I
I
#
#
1
=
(
)
(
)
Ê $'\
"$ \
Ð\
Ñ
Ê
Ð\
Ñ
"$ \
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- Spring '09
- Forgot
- Math, Deposit account, Geometric progression, Residual, Dose, Exponential decay, Eventual Maximum Residual
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