Answer:
The surface area of the balloon is [tex]S(t) = \frac{100}{49} \pi t^8[/tex]
Step-by-step explanation:
Given;
S(r) = 4πr²
where;
S is the surface area of the balloon
r is the radius of the surface
The radius of the balloon at time "t" is given as;
[tex]r(t)= \frac{5}{7} t^4 \ \ \ t\geq 0[/tex]
The surface area of the balloon as a function of time "t" is calculated as;
[tex]S(t) = 4\pi (\frac{5}{7} t^4)^2\\\\S(t) = 4\pi (\frac{25}{49} t^8)\\\\S(t) = \frac{100}{49} \pi t^8[/tex]
