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noname [10]
3 years ago
6

A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 40° F. Af

ter one-half minute the thermometer reads 60° F. What is the reading of the thermometer at t = 1 min? (Round your answer to two decimal places.)
Mathematics
1 answer:
fgiga [73]3 years ago
5 0

Answer:

53.3324

Step-by-step explanation:

given that a  thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 40° F.

By Newton law of cooling we have

T(t) = T+(T_0-T)e^{-kt}

where T (t) is temperature at time t,T =surrounding temperature = 40, T0 =70 = initial temperature

After half minute thermometer reads 60° F. Using this we can find k

T(0,5) = 40+(70-40)e^{-k/2} = 60\\e^{-k/2} =2/3\\-k/2 = -0.4055\\k = 0.8110

So equation is

T(t) = 40+(30)e^{-0.8110t}\\

When t=1,

we get

T(1) = 40+(30)e^{-0.8110}\\\\=53.3324

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