Answer
$f(t)=16\pi t^2$
Where $f(t)$ represents surface are, for given $t$ time (in seconds).
Work Step by Step
We know the formula for surface area of a sphere:
$A=4\pi r^2$
Let's say that $f(t)$ is the surface area of the balloon.
To formulate the function, we have to express the radius in terms of $t$. The radius expands by $2cm$ every second, so the radius is :
$r= 2t$
Now we can write:
$f(t)=4\pi(2t)^2=16\pi t^2$