Question

Please assist, I'm really bad with word problems

Answer 1

The surface area of the balloon is
`S(t) = (100)/(49) \pi t^8`

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)= (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 ((5)/(7) t^4)^2\\\\S(t) = 4\pi ((25)/(49) t^8)\\\\S(t) = (100)/(49) \pi t^8`