Question

The temperature T of a body will increase or decrease at a rate
proportional to the temperature difference respectively below or
above the surrounding temperature, T¯, the constant of
proportionality being k. Derive an expression depicting the
temperature of the body as a function of the time given that its
initial temperature is T_{0}. Sketch, by inspection, the
graph of T = T(t) when T_{0} < T¯, and when
T_{0} > T¯.

Answer #1

Suppose the rate of change of the temperature of a body is
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. The k initial body temperature is 120 After 40 minutes, the
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a.) Find the differential equation with initial condition that
models this situation.
b.) Solve to find the general solution using the technique of
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Newton's Law of Cooling tells us that the rate of change of the
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(1 point) Newton's Law of Cooling states that the rate of
cooling of an object is proportional to the temperature difference
between the object and its surroundings. Suppose t is time, T is
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However, he has colour blindness and cannot tell whether the burger
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Recall that this Law states that "The rate of change of the
temperature of an object is proportional to the difference between
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1. Solve the given initial value problem. dy/dt = (t^3 +
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