- #1

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**Problem**

From Newton's Law of Cooling, we can use the differential equation

dT/dt= -k(T-T

_{s})

where T

_{s}is the surrounding temperature, k is a positive constant, and T is the temperature.

Let [tex]\tau[/tex] be the time at which the initial temperature difference T

_{0}-T

_{s}has been reduced by half. Find the relation between k and [tex]\tau[/tex].

**Work**

I have found the temperature equation for the object to be

T(t) = T

_{s}+ (T

_{0}-T

_{s})e

^{-kt}

If the initial temperature difference is reduced by half, i tried

T(t) = T

_{s}+ 0.5(T

_{0}-T

_{s})e

^{-kt}

but couldn't solve it any further. Could someone please shed some light on what i should do next?