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Unformatted text preview: this situation, we know the
physical limit of the temperature of the coﬀee is room temperature,11 and the diﬀerential equation
which gives rise to our formula for T (t) takes this into account. Whereas the radioactive decay
10 The time it takes for half of the substance to decay.
The Second Law of Thermodynamics states that heat can spontaneously ﬂow from a hotter object to a colder
one, but not the other way around. Thus, the coﬀee could not continue to release heat into the air so as to cool below
11 6.5 Applications of Exponential and Logarithmic Functions 383 model had a rate of decay at time t directly proportional to the amount of the element which
remained at time t, Newton’s Law of Cooling states that the rate of cooling of the coﬀee at a given
time t is directly proportional to how much of a temperature gap exists between the coﬀee at time
t and room temperature, not the temperature of the coﬀee itself. In other words, the coﬀee cools
faster when it is ﬁrst s...
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