The area was 1/32 as great as the area of the original piece of paper. How many cuts did she make?

Question

Jen cut a piece of paper in half and threw away one half.  She cut the remaining paper in half and threw away one half.  She continued doing this until she had a piece of paper whose area was 1/32 as great as the area of the original piece of paper. How many cuts did she make?

Answer 1

Letting the beginning area = 1 for a whole sheet,

Your basic function for the area is:

 

Area = 1/2^c   where c = # cuts made

 

Zero cuts A = 1/2⁰ = 1

1 cut:  A = 1/2¹= 1/2

2 cuts: A = 1/2² = 1/4

 

The equation you are solving is:

 

1/2^x = 1/32

cross multiply

2^c = 32

c=5

Answer 2

what we have here is a reverse exponential, so if we focus solely on the denominator we need

2^x = 32

1. 32/2 = 16

2. 16/2 = 8

3. 8/2 = 4

4. 4/2 = 2

5. 2/2 = 1

 

2⁵ = 32, and ⁵√32 = 2

So 5 cuts were made.