Step 1 :Given the surface area formula for a sphere with radius r: \(S(r) = 4 \pi r^{2}\)
Step 2 :Given the radius formula for the balloon after t seconds: \(P(t) = \frac{4}{3}t\)
Step 3 :Substitute the radius formula into the surface area formula: \(N(t) = 4 \pi (\frac{4}{3}t)^{2}\)
Step 4 :\(N(t) = 4 \pi (\frac{16}{9}t^{2})\)
Step 5 :\(N(t) = \frac{64}{9} \pi t^{2}\)
Step 6 :\(\boxed{N(t) = \frac{64}{9} \pi t^{2}}\)