A couple coffee changes from a temperature of 75ﾟC to 12ﾟC what is the change in temperature in ﾟC

Explanation:

Answer

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The initial temperature of the coffee T0=100∘C.

The temperature of the room 15∘C.

Let T be the temperature at time t in minutes.

By Newton's law of cooling,

dtdTα(T−15)

∴dtdT=k(T−15)

⇒T−15dT=kdt

⇒∫T−15dT=∫kdt

⇒log(T−15)=kt+logc

⇒log(cT−15)=kt

⇒T−15=cekt

At t=0,T=100

We have 100−15=ce0⇒85=c

Thus we get T−15=85ekt.

When t=5minutes,T=60

⇒60−15=85e5k.

⇒e