Question

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?

Answer 1

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

$4=17e^{-0.4353*t}$

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

$3.32min=t$