A cup of soup cooled from 90 to 60 degrees in 10 min in a 20 degree room. Use Newton's Law of Cooling to find how long it will take the soup to cool to 35 degrees when placed in a -15 degree freezer.

Question

A cup of soup cooled from 90 to 60 degrees in 10 min in a 20 degree room.  Use Newton's Law of Cooling to find how long it will take the soup to cool to 35 degrees when placed in a -15 degree freezer.

anonymous · Answer

ah, these are fun ones.

anonymous · Answer

What has me here is that the k you get from the first equation shouldn't be the k used in the second equation, right?

anonymous · Answer

I believe the k will stay the same

anonymous · Answer

so did you first solve $$40=70e ^{-10k}$$ for k?

anonymous · Answer

Correct.

anonymous · Answer

you should be on the right track then using k=0.056

anonymous · Answer

i get 13.25 minutes

anonymous · Answer

That's what I got as well.  I have another question if you're up for it: A gorilla habitat can support no more than 250 gorillas.  28 gorillas were initially in the habitat. Assume the rate of growth is $$dP/dt=.0004P(250-P)$$ where t is in years.  Derive a formula for the gorilla population in terms of t using partial fractions.