Differential Equations: Mixed MCQ

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MixedHardQuestion 370012

Question

Newton's law of cooling: dT/dt = −k(T−T₀). After solving, T(t) is:

T₀ + (T_initial − T₀)e^(−kt)

dT/dt = −k(T−T₀). Let u = T−T₀: du/dt = −ku → u = Ae^(−kt) → T−T₀ = (T_i−T₀)e^(−kt) → T = T₀ + (T_i−T₀)e^(−kt). As t→∞, T→T₀.