# Thread: A person is murderd!!(Differentiation..

1. ## A person is murderd!!(Differentiation..

I have the following problem, Im not sure this is a calculus problem but I didnīt know where else to post it...

A body is found in a room with the temperature 5degrees.
Att 06.00 the body temperature is 23 degrees
att 08.00 the temperature is found to be 18.5degrees.
When did the murder occur?

Suppose to you Newtons cooling law: y' =-k(y-yg) there yg = temperature of the room...

Well so I have y' = -ky +ky(g) = y' +ky = 25k

So the general solution is y = Ce^(kx)

The body temp at the murder was 37degrees

And here Im stuck....

Also I donīt want to getting any more warnings so does anyone know how I report the post? So I can tell the admin I didnīt know where to post it?

2. Originally Posted by Henryt999
I have the following problem, Im not sure this is a calculus problem but I didnīt know where else to post it...

A body is found in a room with the temperature 5degrees.
Att 06.00 the body temperature is 23 degrees
att 08.00 the temperature is found to be 18.5degrees.
When did the murder occur?

Suppose to you Newtons cooling law: y' =-k(y-yg) there yg = temperature of the room...

Well so I have y' = -ky +ky(g) = y' +ky = 25k

So the general solution is y = Ce^(kx)

The body temp at the murder was 37degrees

And here Im stuck....
$\displaystyle \frac{dy}{dt} = -k(y - 5)$

$\displaystyle \frac{dy}{y-5} = -k \, dt$

$\displaystyle \ln(y-5) = -kt+C$

$\displaystyle y-5 = Ae^{-kt}$

$\displaystyle y = 5 + Ae^{-kt}$

let $\displaystyle t = 0$ be 6:00

$\displaystyle 23 = 5 + Ae^{0}$

$\displaystyle A = 18$

$\displaystyle y = 5 + 18e^{-kt}$

$\displaystyle 18.5 = 5 + 18e^{-2k}$

$\displaystyle k = \frac{1}{2}\ln\left(\frac{18}{13.5}\right) \approx 0.1438$

now solve for $\displaystyle t$ ...

$\displaystyle 37 = 5 + 18e^{-kt}$

you should get a negative value indicating the time lapse before 6:00

Also I donīt want to getting any more warnings so does anyone know how I report the post? So I can tell the admin I didnīt know where to post it?
this problem belongs in differential equations.

to report a post to a mod, click on the small red triangle in the upper right corner.

3. ...So are the Police hiring mathematicians now?

*(or is it just this problem that comes within a silly package? )