2 (e) What is the size of the population after 52 hours? 6. A bottle of red wine at a room temperature (27°C) is placed in the refrigerator (5°C). In 6 minutes the wine is chilled to 22°C. (a) Write a differential equation that models the rate of change of the temperature, dTdtWhat law did you use? (b) Find the temperature of wine at a time t. (c) How long does it take for the wine to reach 17°C? 7. Assume the outside temperature varies as a sine wave with a minimum of 32°F at midnight and a maximum of 68°F at noon. (a) Find the function ( )M tin the form 0cosMBtω−that represents the temperature outside at a time t. (b) Write a differential equation for the rate of change of the temperature at a time t in a storage building without heating/air-conditioning and no additional sources of heat (0H=). What Law did you use? (c) Find the temperature ( )T tat a time t if the time constant for the building is 4 hr. (d) Assuming that the exponential term dies out, what is the highest and what is the lowest temperature inside the building? 8. An object of mass 10 kg is given an initial downward velocity of 20 m/sec and then allowed to fall under the influence of gravity. Assume that the gravitational force is constant, with 29.81/ secgm=, and the force due to air resistance is proportional to the velocity of the object with the proportionality constant 10b=N-sec/m. .