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ewton's Law of Cooling and Heating. Suggested time: 15 minutes A cup of coffee is cooling off in a room at temperature 20C. It is assumed the temperature of the coffee T is modeled by Newton's Law of Cooling and has cooling constant 0. 1min (this means k = -0.1). A few drops of very potent poison has "accidentally" been dropped into the coffee. The amount of poison added is so small that it does not affect the cooling constant of the coffee. Note: You may leave your answers in the exact form, i.e., as an expression that contains powers of e and/or logarithms. (a) If poison was dropped in the coffee when the coffee's temperature was 90C, and the poison becomes activated when the temperature drops below 65C, how long until the coffee-poison mixture becomes fatal