| Problem |
Solution |
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1) There is a population of 832 rabbits in the city of Lakewood. The population of rabbits doubled every six months. What was the population of rabbits 30 months ago?
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30 months ago is 5 doubling cycles (30/6 = 5)
There are 2 ways to solve this problem:
- Method 1: Brute force! Use your calculator to successively divide 832 5 times by 2 =
26 rabbits
- Method 2: Use powers of 2:
Let P = the rabbit population 30 months ago.
Write the equation for P and solve:
P x 25 = 832
P = 832 / 25 = 832/32 = 26
P = 26 rabbits.
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2) What is the next term in this sequence:
1, 2, 2, 4, 8, 32, 256, __ ?
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- Each term is the product of the previous 2 terms
- The next term is 256 x 32 = 8192
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3) Study the sequence of shapes below built out of squares. How many squares would be in the 10th
term of the sequence?
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Let n = the term number (1, 2, 3, ...)
- The top row is 3n
- The bottom vertical squares are n
- The ones in between are n(n-1)
- So the total number of squares in the nth term is:
3n + n + n(n-1) =
4n + n2 - n =
3n + n2
- Test this on the first 3:
for n=1: 3+1 = 4
for n=2: 6+4 = 10
for n=3: 9+9 = 18 It works!
- So, the 10th term is 3(10) + 102 = 130
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4) A ladybug is walking along the bottom edge of
a window frame. The y-axis shows distance
from the corner of the window frame in inches.
The x-axis shows time in seconds. How fast is
she walking?