College Algebra: "The surface area S of a hot-air balloon is given by S(r)=4(pi)r2 where..."

[absofruitlyt]

The surface area S (in square meters) of a hot-air balloon is given by S(r)=4πr2 where r is the radius of the balloon (in meters). If the radius r is increasing with time t (in seconds) according to the formula r(t)=(5)/(6)t^(4)(Five-sixths times t to the power of 4), t≥0, find the surface area S of the balloon as a function of the time t.

So Find S(t)

I am usually pretty good at composite functions, but I am horrible at word problems...

 

[stapel]

The surface area S (in square meters) of a hot-air balloon is given by S(r)=4πr2 where r is the radius of the balloon (in meters). If the radius r is increasing with time t (in seconds) according to the formula r(t)=(5)/(6)t^(4)(Five-sixths times t to the power of 4), t≥0, find the surface area S of the balloon as a function of the time t.

So Find S(t)

I am usually pretty good at composite functions, but I am horrible at word problems...

They've given you [imath]r(t)[/imath] and [imath]S(r)[/imath], and asked you to find [imath]S(t)[/imath]. The "word problem" stuff is fluff surrounding that. Just do the composition for which they've asked, using the functions they've given you.

 

[blamocur]

according to the formula r(t)=(5)/(6)t^(4)(Five-sixths times t to the power of 4),

To help you with your word problem I am typesetting it properly: [math]r(t) = \frac{5}{6}t^4[/math]

 

[Steven G]

Don't write r2, instead write r^2
They want what S equals to only have t's in it. You are given a formula for S that has only r's in it. So you want to replace r's with t's. Do you have an equation that converts r's to t's?????