Question 1078775: a dish of lasagna baked at 350 degrees is taken out of the oven into a kitchen that is 68 degrees. After 7 minutes, the temperature of the dish is 299.8 degrees. what will its temperature be 12 minutes after it was taken out of the oven? Round to the nearest degree.
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! Newton’s Law of Cooling Formula is expressed by
T(t) = Ts + (T0 – Ts) e-Kt
Where,
t = time,
T(t) = temperature of the given body at time t,
Ts = surrounding temperature,
To = initial temperature of the body,
k = constant.
So:
T(7)=68+(350-68)e^-kt
299.8=68+282e^-7k
e^-7k=0.82198581560283687943262411347518
ln e^-7k=ln 0.82198581560283687943262411347518
-7k=-0.1960321400324622534737708260656
k=0.02800459143320889335339583229509
Then:
T(12)=68+(350-68)e^-12(0.02800459143320889335339583229509)
T(12)=68+(282)0.71458373316960990812286116751929
T(12)=269.512 degrees 12 minutes out of the oven. ☺☺☺☺
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