SOLUTION: I have to extend a function table to 5,6,7 X. Y 1. 1 2. 1+2 3. 1+2+4 4. 1+2+4+8 Then simplify the the expressions. Then write an equation that relates x an

Algebra ->  Functions -> SOLUTION: I have to extend a function table to 5,6,7 X. Y 1. 1 2. 1+2 3. 1+2+4 4. 1+2+4+8 Then simplify the the expressions. Then write an equation that relates x an      Log On


   

Question 639539: I have to extend a function table to 5,6,7
X. Y
1. 1
2. 1+2
3. 1+2+4
4. 1+2+4+8
Then simplify the the expressions.
Then write an equation that relates x and y when the value of x=15


Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
 X. Y                        Y
 1. 1                    =   1
 2. 1+2                  =   3
 3. 1+2+4                =   7
 4. 1+2+4+8              =  15
 5. 1+2+4+8+16           =  31
 6. 1+2+4+8+16+32        =  63
 7. 1+2+4+8+16+32+64     = 127
 8. 1+2+4+8+16+32+64+128 = 255

The simplified table looks like this:

 X.   Y                        
 1.   1
 2.   3
 3.   7
 4.  15
 5.  31
 6.  63
 7. 127
 8. 255

Notice that each number in the Y column is 1 less than
a power of 2.

 X.   Y                        
 1.   1 = 1 less than   2 = 21 - 1
 2.   3 = 1 less than   4 = 22 - 1
 3.   7 = 1 less than   8 = 23 - 1
 4.  15 = 1 less than  16 = 24 - 1
 5.  31 = 1 less than  32 = 25 - 1
 6.  63 = 1 less than  63 = 26 - 1
 7. 127 = 1 less than 128 = 27 - 1
 8. 255 = 1 less than 256 = 28 - 1

  I'll remove the middle
two columns to make it clearer:

 X.   Y                        
 1. 21 - 1
 2. 22 - 1
 3. 23 - 1
 4. 24 - 1
 5. 25 - 1
 6. 26 - 1
 7. 27 - 1
 8. 28 - 1

Observing the pattern, we see that in every case the exponent
of 2 is the same as the value of x.  So that will have to be the
case when x=15, and we can jump to line 15

15. 215 - 1

Punching that out on a calculator gives 32767

A general equation that relates all values of x and y is

 y = 2x - 1

Edwin