By Newton’s law of cooling the temperature T of a cooling object as a function of time is

TO - initial temperature,

T1 is ambient temperature (meaning the temperature outside the cooling object)

k is constant

W

-32C was the te,perature when electricity was cut off and heating of a house stopped working. After 2 hours from the power cut the inside temperature was measured to be 19,2 C, and after that the following measurements were done:

2,5 hours: 18,3 oC

3,0 hours: 17,5 oC

3,5 hours: 16,6 oC

4,0 hours: 15,8 oC

4,5 hours: 14,9 oC

5,0 hours: 14,2 oC

Supposing Newton’s cooling law to be valid in this case,

Search:

k

T0 initial temperature (which is the temperature at moment t=0 when the power was cut off). Try also to predict when the inside temperature will be dropped below zero.

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my attempt:

19.2-(-32)=(T0-32)e-k(2)

14.2-(-32)=(T0-32)e-k(5)

51.2 (T0-32)e-k(2)

46.2 (T0-32)e-k(5)

1.11 e2,5k

k= 0.041103894

k= ln(1.11)/2.5

Substitude k into the first equation

51.2=(T0-32)e-2k

51.2=(T0-32)e-2((ln(1,11)/2,5))

and now ?????????????