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Arturiano [62]
3 years ago
13

A thermometer is taken from a room where the temperature is 20°C to the outdoors, where the temperature is 3°C. After one minute

the thermometer reads 11°C. (Round your answers to one decimal place.)
(a) What will the reading on the thermometer be after one more minute?

(b) When will the thermometer read 4°C?
Mathematics
1 answer:
IrinaVladis [17]3 years ago
6 0

Answer:

A. T=7.12°C; B. t=3.32min

Step-by-step explanation:

In order to find the answer we can use the Newton's law of cooling:

y(t)=y0e^{kt} where:

y0=initial temperature - room temperature

k=coefficients

t=time

Because the outdoors temperature is 3°C, the initial temperature is 20°C, and because the thermometer reads 11°C after 1min we have:

11=(20-3)e^{k*1}

ln(11/17)=k

-0.4353=k

A. Temperature after an extra minute.

y(2)=17e^{-0.4353*2}

y(2)=7.12 so the answer is 7.12°C

B. Time in order to read 4°C

4=17e^{-0.4353*t}

ln(4/17)/(-0.4353)=t}

3.32min=t

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