Question

Please assist, I'm really bad with word problems

Answer 1

Answer:

The surface area of the balloon is $S(t) = \frac{100}{49} \pi t^8$

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;

$r(t)= \frac{5}{7} t^4 \ \ \ t\geq 0$

The surface area of the balloon as a function of time "t" is calculated as;

$S(t) = 4\pi (\frac{5}{7} t^4)^2\\\\S(t) = 4\pi (\frac{25}{49} t^8)\\\\S(t) = \frac{100}{49} \pi t^8$