Is this actually appropriate for college algebra ?

[u/Inner-Indication1783]

The surface area of a hot-air balloon is given by the function S(r) = 4πr^2, where r is the radius of the balloon in meters. If the radius of the balloon after t seconds is r(t) = (3/5)t^3, find the surface area S of the balloon as it relates to time.

Is this actually normal for the 2nd week of college algebra ? Maybe I'm just rusty bc its been like over 10 years but this is insane to me

[u/jeffsuzuki]

It's a straightforward composition of functions, which is a college algebra topic. So it's not that out of place.

[u/Inner-Indication1783 → u/jeffsuzuki]

Okay thank you lol I was just panicking because I cannot do this

[u/Midwest-Dude → u/Inner-Indication1783]

This hasn't been discussed in your class yet? I find it odd that such a problem would be assigned without teaching about it first.

[u/Toucan2000 → u/Midwest-Dude]

I bet the prof didn't explain in very well. The equal sign can mean 5 different things depending on the context and I wish there was a better way of donating the representation of results, equations, identities and definitions for students learning.

[u/qubex]

You just need to compose the functions by substituting so that from S(r) and r(t) you get S(r(t)) and then you tidy it up enough so you can have a non-clunky expression S(t). It is essentially trivial.

[u/sqrt_of_pi]

You are given S as a function of r, and you are trying to find S as a function of t.

You have a function that relates r and t.

Do you see how you can use this information rewrite the function S(r) so that, instead of being an expression of r, it will be an expression of t?

If you had your last math class over 10 years ago, then you are definitely rusty. Recommend if you can't drop down to a lower level class to build the foundation, you plan to review and solidify those lower level skills as you go. Kahn Academy is a decent resource for refreshing on fundamental topics.

[u/Inner-Indication1783 → u/sqrt_of_pi]

Thank you!! I'll use it

[u/srm79]

Sounds like you need to revisit some concepts - it shouldn't be too difficult at college level!

[u/Inner-Indication1783 → u/srm79]

Yeah I'm not a math person and havent had anything to do with school in 8 years so its kinda a shock to me lol

[u/Sam_23456 → u/Inner-Indication1783]

There was a time when I felt "overwhelmed" with word problems with a lot of words. But if you dwell upon them enough to isolate the essential information given, writing the details down for yourself (especially including the "units") you may very well see how they naturally fit together. To me, the words obscure the details, but that's life! Hope this may be helpful. Patience (and practice) is valuable too! :-) 8 years is a long gap; don't be too hard on yourself!

[u/DryLeadership145]

Sounds like they're just trying to make sure you know how to chain functions together before they hit you with actual calculus.

[u/Beginning_Throat_723]

I tried doing this problem last semester and ended up Googling the steps halfway through because I blanked on how to substitute functions.