Question

Which kind of function best models the data in the table? Use differences or ratios.

x | y
0 | 0.6
1 | 4.2
2 | 29.4
3 | 205.8
4 | 1440.6

A. exponential
B. quadratic
C. linear
D. none of the above

I can't decide which one, but I think it's b.

Answer 1

You can only "decide" after you have done some analysis, you appear to
be just guessing.

Is there a common difference between consecutive y values ?
if so , you have a linear.
is there a common ration between consecutive y values?
if so, you have an exponential.

Did you check for those properties???

Answer 2

y(n+1) = 7 y(n)
y = a b^ x
if x = 0 y = 0.6 = a b^0 = a
so
y = 0.6 b^x
if x = 1, y = 4.2
4.2 = 0.6 b^1 = 0.6 b
so
b = 7
so
y = 0.6 * 7^x
==================
check
if x = 3
y = 0.6 * 7^3 = 205.8 sure enough