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A car engine runs at a temperature of 87°C, when the engine is turned off, it cools according to Newton’s Law of Cooling (T=Ts+D0e-kt) with constant k=0.0347, where the time is measured in minutes. How long does it take for the engine to cool to 33°C if the surrounding temperature is 15°C. (A) 44min (B) 42min (C) 40min (D) 38min (E) 36min (note: ln2=0.6931)

They gave you the formula and the numbers, so just solve for t when T=33

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Did you know that a car engine cools according to Newton's Law of Cooling? When a car engine is turned off, it cools down with a constant rate, given by the equation T = Ts + D0e-kt. In this equation, T represents the temperature of the engine at any given time, Ts represents the surrounding temperature (in this case, 15°C), D0 is the initial difference in temperature between the engine and the surrounding, k is the constant rate of cooling (0.0347 in this case), and t represents the time in minutes. Using this equation, we can calculate how long it takes for the engine to cool down to a certain temperature. In this scenario, we need to find out how long it takes for the engine to cool down to 33°C. By substituting the given values into the equation, we can solve for t. Using the given options, we can determine that it takes 40 minutes for the engine to cool down to 33°C. (C) 40min.