A liquid at temperature $ f $ is placed in an oven at temperature $ T_o $. The temperature of the liquid increases at a rate proportional to the difference between the temperature of the liquid and that of the oven.

Write a differential equation for the temperature $ T(t) $ of the liquid.

To write a differential equation for the temperature t(t) of the liquid, we can use the given information. The temperature of the liquid increases at a rate r times the difference between the temperature of the liquid and that of the oven. Let's denote the temperature of the liquid as T and the temperature of the oven as Toven. The differential equation can be written as dT/dt = r(T - Toven).

If T denotes the temperature of the liquid, and A the oven temperature, and r the rate constant, the mathematical representation of this idea is given by the differential equation: dT/dt = r*(A - T). This equation is based on Newton’s law of cooling and similar principles can also be applied in other disciplines such as chemistry and physics.

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A liquid at temperature \( f \) is placed in an oven at temperature \( T_o \). The temperature of the liquid increases at a rate proportional to the difference between the temperature of the liquid and that of the oven. Write a differential equation for the temperature \( T(t) \) of the liquid.

Answer :

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A liquid at temperature \( f \) is placed in an oven at temperature \( T_o \). The temperature of the liquid increases at a rate proportional to the difference between the temperature of the liquid and that of the oven.

Write a differential equation for the temperature \( T(t) \) of the liquid.