A glass of water with an initial temperature of 25 degrees F is placed in a room with a surrounding temperature of 70 degrees F. After 1 hour, the temperature of the water is 40 degrees F. To the nearest whole number, find the temperature of the water after 5 hours. Round the value of \( k \) to the nearest four decimal places.

Options:
A. 67 degrees F
B. 70 degrees F
C. 65 degrees F
D. 62 degrees F

To find the temperature of the water after 5 hours, we need to use Newton's Law of Cooling. Newton's Law of Cooling states that the rate of change of temperature of an object is proportional to the difference between its own temperature and the temperature of its surroundings. The formula for Newton's Law of Cooling is given by: T(t) = Ts + (T0 - Ts) • e^(-kt), where T(t) is the temperature at time t, Ts is the surrounding temperature, T0 is the initial temperature, and k is the constant of proportionality.

In this case, the initial temperature (T0) is 40°F, the surrounding temperature (Ts) is 70°F, and we know that after 1 hour, the temperature decreased to 40°F. We can plug in these values to find the constant k. Once we have k, we can determine the temperature of the water after 5 hours by plugging in t = 5 into the formula.

The correct answer is 62 degrees F (Option D).