[cow7dvd]

okay so there is a problem in my math book, it goes like this:
One day in an ancient kingdom, a peasant saved the life of the king's daughter. The king was so grateful that he told the peasant anything she desired. The peasant--who was also the kingdom's chess champion--made an unusual request.
"i would like you to place 1 coin on the first square of my chessboard, 2 coins on the second square, 4 on the third square, 8 on the fourth square, and so on until you have covered all 64 squares. Each square should have double the coins as the last square."
I drew a graph of the data and the points are this:
(1,1) (2,2) (3,4) (4,8) (5,16) (6,32) (7,64) (8,128) (9,256) (10, 512)
now I need to make an equation of this line, now the only thing that confuses me on how to do this is that there is ABSOLUTELY NO Y-INTERCEPT this is because the x-axis is which number square you are putting the coins on, and since there is no "0th square" there can be no point in which the line passes the y-axis, I know that the equation will include something ALONG THE LINES of 2 to the power of x(2^x) but I know that it isn't just plain that because 2^1 is 2, not 1, even if you subtract 1 from it like this (2^1)-1 it becomes a problem at 2, (2^2)-1=3, not 2, and it isn't 2^x-x, because it gets to be a problem at 3, (2^3)-3=5, not 4. sorry for this long explanation, but I want to get everything covered. Please help, I need to write this equation...

[ebaines]

You have noted that the y value is something similar to 2^x, but it's not quite right. If you wrirte out a table of x and y values using y = 2^x, and compare it to the points you were given, you'll see that 2^x is off by one row:

x y 2^x
1 1 2
2 2 4
3 4 8
4 8 16
etc.

The independent variable (x) in y = 2^x is off by one. So try this: see what happens if you subtract 1 from x, so that the exponent is (x-1). What happens?

By the way, the y intercept for this function is the value for x=0. You haven't been explicitly told what this is, but since the value on any one day is half of the value of the next day, it stands to reason that on day 0 the peasant would have 1/2 of the coins he has on day 1, or 1/2 of a coin. Since that is not possible, we don't worry about the y intercept in this problem..