An object is taken out of a 21 degree C room and placed outside where the temperature is 4 degree C. Twenty-five minutes later the temperature is 17 degree C. It cools according to Newton's Law. Determine the temperature of the object after one hour. Round to the nearest tenth of a degree.

The temperature of the object after one hour is 12.9°C to the nearest tenth of a degree

Step-by-step explanation:

Please see the attachments below

12.9 degree C

Step-by-step explanation:

1 hour = 60 minutes

So the Newton's law of cooling state that the rate of changing in temperature is proportional to the different in temperature, in other words:

where t is the time in minute, k is the cooling constant and is the environmental temperature. This differential equation can be solved to have a form of

where is the initial temperature.

We know that at 25 minutes T(25) = 17

So after 60 minutes:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2