Question

What is the pattern in this table? (x- 1, y- 1) (x- 2, y - 3) (x- 3, y- 7) (x- 4, y- 15) (x- 5, y- 31) And can you make an equation for it?

Answer 1

the first coordinate looks like \(x-n\) for \(n=1,2,3,...\)

Answer 2

now how about the numbers 1, 3, 7, 15, 31, ...
do they ring a bell?

Answer 3

i am going to guess that the answer is "no" because it is not so obvious

Answer 4

it would probably look like y = x plus what times what etc... like that and yeah they are the ys

Answer 5

it is not so clear what the patter for the second number are
but if you add one to each, it might be more clear
\[2,4,8,16,32,...\]

Answer 6

what i meant to say is "it is not so clear what the pattern for the second numbers is"

Answer 7

do you recognize \(2,4,8,16,32,...\)?

Answer 8

Nope

Answer 9

you double one number to get the next

Answer 10

oh yeah but how do I put that in an equation like y = x times what plus what etc.

Answer 11

like this \(2^n\) for \(n=1,2,3,...\)
then you have to subtract \(1\) so it would really be \(2^n-1\)

Answer 12

so a "final answer" might be something like \[(x-n,y-(2^n-1))\]

Answer 13

or if you want to distribute the minus sign you could write
\[(x-n,y-2^n+1)\]

Answer 14

it is a little tricky because the variable is in the exponent, not on the ground floor like say \(3n-5\) or something