Answer:
y = 2 * 4^x
Step-by-step explanation:
We could define a wide variety of rules!
It turns out that any set of n (x, y) pairs can be modeled by a singular polynomial of degree (n-1) or less, and by infinitely many polynomials of degree n or more! And we're only talking polynomials!
Let's input it into a polynomial interpolation calculator:
[tex](27 x^4)/4 - (63 x^3)/2 + (225 x^2)/4 - (51 x)/2 + 2[/tex]
Well I don't love this.
Let's try to actually look for patterns. We see that the function is rapidly increasing. More and more, actually. Let's look for the ratios of each next y
8/2 = 4
32/8 = 4
128/32 = 4
512/128 = 4
BINGO!
So we can define the rule as:
y = 2 * 4^x
