A function satisfies $f(x+y)=f(x)\cdot f(y)$ for all real $x$ and $y$, and $f(1)=3$. Then $f$(4) equals:

Apply the rule repeatedly: $f(2)=f(1+1)=3\times 3=9,f(3)=f(2+1)=9\times 3=27$ and $f(4)=f(3+1)=27\times 3=81$ — that is, $f(n)=3$ⁿ. (12 treats the rule as $f(4)=4f(1)$; 27 is $f$(3), one step short; 243 is $f$(5), one step too many.) A function that fits is $f(x)=3$ˣ, and $3^4=81$.