Actually I have two questions. I am trying to help my son with his algebra and we are both stumped. Please help, this is due tonight.

Use the table to complete each part.
X Y
1. 1
2. 1+2
3. 1+2+4
4. 1+2+4+8
5
6
7
a. Extend the above table by writing expressions for y when x=5, 6, and 7.
b. Simplify each expression for y in your table from part a. What pattern do you notice in the simplified expressions?

Question

Actually I have two questions.  I am trying to help my son with his algebra and we are both stumped.  Please help, this is due tonight.  

Use the table to complete each part.
X                         Y
1.                         1
2.                         1+2
3.                         1+2+4
4.                         1+2+4+8
5
6
7
a.  Extend the above table by writing expressions for y when x=5, 6, and 7.
b.  Simplify each expression for y in your table from part a.  What pattern do you notice in the simplified expressions?

mertsj · Answer

5.  1+2+4+8+16
6.  1+2+4+8+18+32
7.  1+2+4+8+16+32+64

anonymous · Answer

Hi.
recognize that the patterns under the y row, is just and addition of something thats a multiple of 2. 1+2+(2*2)+(2*2*2)+....

mertsj · Answer

1.  y=1
2.  y=3
3.  y=7
4.  y=15.  
5.  y=31
6.  y=63
7.  y=127

mertsj · Answer

You add a power of two each time.

anonymous · Answer

Thanks everyone for your answers.  One more question for this problem.
C. Write an equation the relates x and y.  Use your equation to find th value of y when x=15.

mertsj · Answer

$$y=2^x-1$$