Royce is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is doubled. The paper starts out flat, with a thickness of 2 millimeters.
A. Write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. Explain how you came up with your ordered pairs.
B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A.

Question

Royce is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is doubled. The paper starts out flat, with a thickness of 2 millimeters. 
A. Write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. Explain how you came up with your ordered pairs. 
B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A.

anonymous · Answer

i already did A

danjs · Answer

The ordered pairs in the first part will be in the form (x,y) = (#folds, Thickness)

The initial condition when x = #folds = 0 ; is y = thickness = 2 mm

anonymous · Answer

number of folds         thickness

      0                               2
      1                               4
      2                               6
      3                               8
      4                              10
      5                              12

danjs · Answer

Do you think this is a function?

anonymous · Answer

yes

danjs · Answer

each value is 2 times the last value, exponential

anonymous · Answer

ooh

danjs · Answer

your points are a little off, they are 2,4,8,16,32,64......

anonymous · Answer

oh, so 2,4
            8,16
etc

anonymous · Answer

so it's double

danjs · Answer

number of folds               thickness 

(0,2)
(1,4)
(2,8)
(3,16)
(4,32)
(5,64)
.
.
.

danjs · Answer

The general form for this type of function is

$$y(x) = A*b^x$$

have you seen that before?

anonymous · Answer

ive seen those type of things with numbers

danjs · Answer

Put in the first point where x=0 and y=2, that will give you the value for the A .
$$y(0) =2= A*b^0 $$

danjs · Answer

b to the zero power = 1, so 

2 = A*1   ...           A = 2

anonymous · Answer

uh do i mulitiply 0 x 2

anonymous · Answer

what

danjs · Answer

Now you know,
$$y(x) = 2 *b^x$$

Now use another point , and figure out what b is

danjs · Answer

The second point is (x,y) = (1 , 4)

$$y(1)=4 = 2*b^1$$

anonymous · Answer

8?

danjs · Answer

$$b^1=2$$

b=2
The overall function becomes,

danjs · Answer

$$y(x) = 2*2^x$$

anonymous · Answer

ohhh

danjs · Answer

It is a function because for all the elements in its domain, (All x values greater than or equal to zero), there is one value in the range, (all y values greater than or equal to 2)

danjs · Answer

What does your book give as the definition for a function?

anonymous · Answer

its not a book @DanJS

danjs · Answer

It is a function because each input x, gives one output, y