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Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage V across its terminals and that, if t is measured in seconds, Solve this equation for V, using to denote the value of V when t = 0. How long will it take the voltage to drop to 10% of its original value?
Newton’s law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton’s law of cooling. If the coffee has a temperature of 200◦F when freshly poured, and 1 min later has cooled to 190◦F in a room at 70◦F, determine when the coffee reaches a temperature of 150◦F.
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