Consider the following model for the cooling of a hot cup of soup where T m (0) Here Tm is the temperature of the soup at any time t 0,is the constant temperature of the surrounding medium, is the initial temperature of the soup, and k is a constant of proportionality depending on the thermal prope...

After separating the variables we obtain dTm Integration y ...

Consider the following model for the cooling of a hot cup of soup: where T m (0)

Question:

Consider the following model for the cooling of a hot cup of soup:

where T_m(0) = α. Here Tm is the temperature of the soup at any time t > 0,βis the constant temperature of the surrounding medium, is the initial temperature of the soup, and k is a constant of proportionality depending on the thermal properties of the soup. We will solve the above differential equation for T_m:

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