Alright, I'm having issues with this problem. You all remember when that lady spilled coffee on herself and then sued mcdonalds for saying it was too hot? Well i have a problem that's based on that. You can view the problem here. Tommy Ratliff - Writing in Calculus (sorry i'm too lazy to type it all out, lol)
Anyways, in essence there are two periods of time. THe first one he's holding the coffee in the cup holder of his car (T(s)=72 degrees F) and then the second one he's holding it in his hands (T(s)=92.3 degrees F). Anyhow, what i wanna do is find an inequality that if he held the cup holder and then his hands for greater than this amt of time then the final temp will be above 140 etc. etc.
So assuming that the entire t will be 10 min (600s) and that the T(0)=160 i set it up like so:
Final T (FT) = 140 <-- that's what we want
and the FT for after he's put it in the cup holder for so long will = the T(0) for when he's holding it in his hands. Hence
T=(160 -72) e^*((600-t)*(ln(.875)/270))+72
140-92.3=(T(0) - 92.3)e^(t*ln(.875)/270) ~ substitute the T(0) for
the expression above
But that didn't work... and it's driving me nuts.... I'm sorry, i know i didn't explain it very well, but if anyone actually gets what i mean and knows what i did wrong or how to do it, then id GREATLY appreciate it.