Since 4 = 2² and 16 = 2⁴, we can start off with the function f(x) = 2ˣ.
But then f(0) = 2⁰ = 1 ≠ 4, and f(2) = 2² = 4 ≠ 16.
To account for this, add 2 to the exponent, so that f(x) = 2ˣ⁺².
Now f(0) = 2⁰⁺² = 2² = 4, and f(2) = 2²⁺² = 2⁴ = 16, as required.
