This is an exponential function.
f(0) = 2 and f(1) = 6
=> f(x) = a•bˣ
f(0) = 2 => a•b⁰ = 2 => a = 2
f(1) = 6 => 2•b¹ = 6 => b = 3
=> f(x) = 2•3ˣ
