Posted by bob on Monday, July 23, 2012 at 12:44pm.
According to the Newton's Law of Cooling we have that:
T(t) = Ts + (To - Ts)*e^(-k*t) ;
t is the time in the preferred units (seconds, minutes, hours, etc.)
T(t) is the temperature of the object at time t
Ts is the sorrounding constant temperature
To is the initial temperature of the object
k is a constant to be found
so let's find k
Before I go any further, there is something very wrong with your data
since water boils at 100° C, there is no way that the coffee could have a temperature of 350°
nor can you drink coffee that has a temp of 280°, it would be very hot steam.
check your question and your typing.
its 35° and 20° sorry :$
Looking at this question again, I think they want this done in a much simpler way.
when t = 35, the T(35) the temperature has decreased by 1.2% each minute,
so temp after 35 minutes = 35(1.015^-35
to have a temp of 28°
35(1.015)^-t = 28
1.015^-t = .8
take log of both sides
log (1.015^-t) = log .8
-t = log .8/log 1.015
-t = -1498
t = appr 15
let me know if we have to use Newton's Law of Cooking equation.
where did you get 1.015 from in the first equation?
also what kind of function is this?
sorry, that was a typo, should have been 1.012
for 1 + 1.2%
I am getting myself all messed up here, I noticed that I used 1.015 several times instead of 1.012
Almost too deep into the mess to recover, I should have done this:
reduce by 1.2% per minute ---- >1 - .012 = .988
35(.988)^35 = 22.9°
when does 35° become 28° ?
35(.988)^t = 28
.988^t = 28/35 = .8
t log .988 = log .8
t = log .8/log .988 = 18.48 minutes
does that make more sense?
You are dealing with an "exponential function"
1 - .012 = .988 why did you do this?
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