Newton's law of cooling states that the rate at which temperature T of a body falls is proportional to the difference in temperature between the body and its surroundings. If t is the time and the surroundings are at 0°C then the differential equation representing the above information is: dT :-kT dt Prove, using integration methods, that the general solution to this differential equation is: T = Ae kt where A and k are constant values If the temperature of an aluminium ingot after it has been cast falls from 900°C to 700°C in 30 seconds, using the differential equation above find the equation for T at any time(t)
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