Question

If the paper were to be cut instead of folded, the height of the stack would double at each successive stage, and it would be possible to continue.

a. Write an expression that describes how many layers of paper result from 16 cuts.
b. Evaluate this expression by writing it in standard form.

Answer 1

65536

Explanation:

a.

1 cut- 2 layers 2^1

2 cuts- 4 layers 2^2

3 cuts- 8 layers 2^3

4 cuts- 16 layers 2^4

...

16 cuts- 2^16

`{2}^(16) = 65536`

b.

for n cuts

`{2}^(n) = m`

being m the amount of layers.

then

`\sqrt[n]{m} = 2`

we can verify

`\sqrt[16]{65536} = 2`