I need help on this calculus problem, bros

[-SD-]

Here it is:
A roast turkey is taken from an oven when its temperature is 185 degrees and is placed on a table in a room where the temp is 75 degrees. The turkey eventually will approach room Temp. After an hour, the turkeys temp. is 125 degrees. By measuring the slope of the tangent, estimate the rate of change of the temp. after an hour.
Note: I have not had Newtons law of cooling, so dont use that please.
The trouble I have is finding the slope of the tangent when no equation of the function is given.

 

[Kakdiesel]

easy superdave

you must construct a Temperature vs. Time graph where Temp is on the y axis, and time is on the x axis..at zero time, the turkey is 185 degrees, at sixty minutes, the temperature isi at 125...therefore y-y1 = m (x-x1) where y1 = 125 and x1 = 60 minutes. And M equals 1 degree/min.

therefore y = x + 65 is the formula for the tangent to this slope

 

[Warik]

Kak... that's algebra man. =)

superdave, look up exponential decay. The temperature of the turkey is decaying and approaching the value 75deg. As time goes on, the rate of change of the temperature gets smaller and approaches 0 (because once the temp of the turkey reaches 75, the turkey won't get any cooler).

Look up exponential decay, determine a formula, and take its derivative where t = 1.

-Warik

 

[HamsterHider]

umm guys i can't help here failed the math entrance exam before college and they made me take algebra one but it was so boring i dropped it after 2 weekd and got a new major that did not require any mathematics

 

[-SD-]

So is Kak right? He seems to just state an equation to a line that contains those two points mentioned, not a slope to a tangent line.

 

[Steelheart]

duh!?

 

[Juice Moose]

Who wants to eat a turkey that is room temperature?

Dig into that motherfucker right now!!

 

[Mdguy]

Warik is right. Use exponential decay :

dT/dt = -k(T-Ti)

where k is a constant; T-temperature, t-time
and Ti is the room temperature (at infinite time)


integrate to find T: T=Ti + (T0-Ti)e*-kt T0-initial temp

use values after one hour to find k and then go back to the intial equation, substitute in the final room temperature, k, and the temperature you are given after one hour and you get the slope of the tangent line

 

[ROIDJUNKIE]

Who wants to eat a turkey that is room temperature?

Dig into that motherfucker right now!!

being out of school for 14 years I would have to say.......Juice Moose is correct

 

[Fonz]

KAK, I thought you were majoring in Chemistry????

Thats a pretty bad mistake to make.

Your equation is linear.

Decay is NOT. It is exponential.

(This is pretty basic btw. Also, chemistry
utilizes a lot of decay curves so I'm still
amazed you got it so wrong)

according to Y= A(exp(b))

So, Turkey at 180 degrees C.
End temp is 125 degrees C.
Room Temp is 75 degrees C.

This is the third law of thermodynamics.
System A(Temp A)+Systrem B(Temp B)
will reach an equilibrium temp after a certain
time.(Of course assuming Temp A <> Temp B)


Warik got it right. You have to figure out the
equation according to the decay equation.
(Substitute the values) and take the derrivative
with respect to Time. DT/dt

Godspeed