Helium is pumped into a spherical balloon at . How fast is the radius increasing after 2 minutes?
I've searched some of the other related rates probs posted on this forum, so I apologize if a question like this has been brought up already.
Basically, I understand I'm looking for , and that .
Now, the rate is 2 and the volume of a sphere is .
Implicitly differentiating V with respect to T gets
I know that the rate the volume increases with respect to time is , and I'm not sure what to do with my 2 minutes (or 120 seconds). Is the volume with respect to time 120 seconds and is the rate with respect to time? That would make more sense I think because the dimensions of cubic feet with a factor of 2 is like a rate and seconds is most definitely a part of time.
However, when I try to solve or and that's incorrect. Since I don't know the volume with respect to time, how can I properly go about solving for the rate with respect to time?