A community for students.
Here's the question you clicked on:
 0 viewing
marigirl
 one year ago
Integration application question:
Please help me, Where can I start?
I know it will be an exponential equation eventually.
A farmer goes out at 7.30 am to check his stock and finds one of his cows dead in the creek. The temperature of the cow is 22 degrees Celsius and the temperature of the creek is 5 degrees Celsius. One hour later the temperature of the cow is 19 degrees Celsius. The normal body temperature of a healthy cow is 38.6 degrees Celsius. When did the cow die?
marigirl
 one year ago
Integration application question: Please help me, Where can I start? I know it will be an exponential equation eventually. A farmer goes out at 7.30 am to check his stock and finds one of his cows dead in the creek. The temperature of the cow is 22 degrees Celsius and the temperature of the creek is 5 degrees Celsius. One hour later the temperature of the cow is 19 degrees Celsius. The normal body temperature of a healthy cow is 38.6 degrees Celsius. When did the cow die?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, perhaps you can start with your model, the exponential decay function\[H(t) = T_0e^{Rt}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0$$T_0$$ will probably be the cows temperature when the farmer found it dead and $$R$$ will be the rate at which heat dissipates from the cows body.

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0t=0 cow's body temperature is 22 t=1 cow's body temperature is 19

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. That allows you to compute R

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0what is with the information about the creek being 5 degrees

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is a good question, however, it seems to be erroneous information since the rate is fixed given the conditions at t = 0 and t = 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is based on your model though.

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0@freckles I would really appreciate your input :)

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0im a bit lost with finding R @RBauer4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Put t = 1, then we get\[22 e^{R} = 19\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1morbid use of cows lol

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0actually im very lost

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0oh please help @ganeshie8 .. its bad enough that i have to read about deceased cows :(

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0there is even a picture of a dead cow in the question!!!!! :( :( :( :( :( this is emotionally disturbing me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The thing is, is that the farmer left it in the creek for another hour after he found it!

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0and took its temperature

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Here is what I would do, take\[H(t) = 22 e^{Rt}\]. Then the problem states that at t = 1, the cows temperature was 19, so equivalently \[H(1) = 22 e^{R} = 19\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We can solve for R explicitly for \[e^{R} = \frac{19}{22} \implies e^{R} = \frac{22}{19} \implies \ln(e^{R}) = R = \ln(22/19)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, now that we have R, all we need to do is put H(t) = 38.6 and find the value of t this corresponds to.

freckles
 one year ago
Best ResponseYou've already chosen the best response.0@marigirl are you ok with the equation @RBauer4 has left you with?

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0it makes sense but i am still considering why the paddock temperature is stated. ill take a photo of the answer and send it to you guys

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1im getting 4:30 am using newton's law of cooling

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0answer in the book states t=3.51

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1right, they are using newton's law of cooling do you want to know how to setup the differential equation and solve it

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0yes please i will also upload the model answer shown

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Let \(y(t)\) represent the temperature of cow \(t\) hours after \(7:30\) am, (time after it was observed for the first time) then the temperature in cow follows the newton's law of cooling: \[y' = k(5y)\tag{1}\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1does that look familiar to you if not, you may replace \(y\) by \(T\)

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0thanks, i am not seeing it now, but i will think about it.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1familiar with separation of variables to solve differential equation ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not that I have never solved such an ODE before, but I was never taught that this particular ODE models cooling. Thanks for the clarification @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1question should explicitly specify the model to use i guess because there are several models...
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.