Question

Need help to write equations for 5, 6 & 7

Answer 1

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.


`y = a(b)^x`

We need to find a and b.
Look at x = 0.
For x = 0, y = 4.


`y = a(b)^x`


`4 = a(b)^0`

Since b^0 = 1, this simplifies to


`4 = a`

Now we know a = 4. We have


`y = 4(b)^x`

Look at x = 1. For x = 1, y = 12.


`12 = 4(b)^1`


`12 = 4b`


`b = 3`

Now that we know a and b, we can write the function.


`y = 4(3)^x`

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.