Question

Does the table represent a linear or an exponential function? Explain.

x
1
2
3
4
y
16
64
256
1024

Answer 1

\[f(x)=4^{x+1}.\]You be the judge!

Answer 2

exponential, even if we didn't know anything about what the function actually is, the growth in f(x) is not a constant factor as x increases by 1, so it cannot be linear, thus it must be exponential since we only have two options