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According to Newton’s law of cooling, the temperature u(t) of an object satisfies the differential equationdu/dt= −k(u−T)where T is the constant ambient temperature and k is a positive constant. Suppose that the initial temperature of the object is u(0)= u0.(a) Find the temperature of the object at any time. (I know how to resolve this)

Respuesta :

jorgezarate

Answer:

[tex]u(t)=T+(u_{0}-T})e^{-kt}[/tex]

Step-by-step explanation:

We know:

[tex]\frac{du}{dt} = -k(u-T)[/tex]

We integrate in order to find u(t):

[tex]\int\limits^u_{u_{0}} {\frac{1}{-k(u-T)} \, du } = \int\limits^t_0 \, dt[/tex]

[tex]ln(\frac{u-T}{u_{0}-T} )=-kt\\[/tex]

[tex]u(t)=T+(u_{0}-T})e^{-kt}[/tex]

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