5) The x-values go up by 1: -2, -1, 0, 1, 2 The y values are always 3 times the previous value. This is an exponential function.
[tex] y = a(b)^x [/tex]
We need to find a and b. Look at x = 0. For x = 0, y = 4.
[tex] y = a(b)^x [/tex]
[tex] 4 = a(b)^0 [/tex]
Since b^0 = 1, this simplifies to
[tex] 4 = a [/tex]
Now we know a = 4. We have
[tex] y = 4(b)^x [/tex]
Look at x = 1. For x = 1, y = 12.
[tex] 12 = 4(b)^1 [/tex]
[tex] 12 = 4b [/tex]
[tex] b = 3 [/tex]
Now that we know a and b, we can write the function.
[tex] y = 4(3)^x [/tex]
Now that you have the function written out, notice the following. In the exponential equation we found, the number raised to x is the number you multiply each y value to get the next y value. In this case, each y value is 3 times the previous one, so you have 3^x. The way you find "a" in the exponential equation is to look at the y-coordinate when x = 0. When x = 0, b^x is 1, so b^x drops out, and you get "a" equal to the y-value. In this case, when x = 0, y = 4, so "a" is 4. With b = 3, and a = 4, you can quickly write: y = 4(3)^x.