4.
Stage 1: 2, Stage 2: 6, Stage 3: 14, Stage 4: 30
5.
Stage
Number of Branches
Pattern
12
2
(
2
1
2
1)
26
2
(
2
2
2
1)
31
4
2
(
2
3
2
1)
43
0
2
(
2
4
2
1)
The formula is twice the difference of 2 to a power
that is the stage number and 1:
A
n
5
2(2
n
2
1).
6.
No, the base of the tree or segment of a branch
without an end does not contain a replica of the
entire tree.
7.
Ï
2
w
<
¬
1.4142…
Ï
Ï
2
w
w <
¬
1.1892…
8.
Ï Ï Ï
2
w
w
w
<
1.0905…; the results are getting closer
to 1, so the result after 100 repeats approaches 1.
9.
Yes, the procedure is repeated over and over
again.
10.
First, write an equation to find the balance after
one year.
current balance
1
(current balance
3
interest rate)
5
new balance
4000
1
(4000
?
0.011)
5
4044
4044
1
(4044
?
0.011)
5
4088.48
4088.48
1
(4088.48
?
0.011)
5
4133.45
4133.45
1
(4133.45
?
0.011)
5
4178.92
After compounding interest four times, Jamir will
have $4178.92 in the account.
Pages 328–331
Practice and Apply
11.
9 holes
12.
73 holes
13.
Yes, any part contains the same figure as the
whole, 9 squares with the middle shaded.
14.
Stage
Number of Dots
Pattern
111
1
0
232
1
1
363
1
3
41
04
1
6
The formula is the stage number plus the number
of dots in the previous stage:
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Harshad number, stage, Prime number, Triangular number, sierpinski triangle

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