For 0 < t < 24 hours, the temperature inside a refrigerator in a kitchen is given by the function W that satisfies the differential equation dW/dt = 3 cos t/2W. W(t) is measured in degrees Celsius (°C), and t is measured in dt hours. At time t = 0 hours, the temperature inside the refrigerator is 3°C.
a. Write an equation for the line tangent to the graph of y=W(t) at the point where t = 0. Us the equation to approximate the temperature inside the refrigerator at t = 0.4 hour.
b. Find y = W(t), the particular solution to the differential equation with initial condition W(0) = 3.
c. The temperature in the kitchen remains constant at 20° for 0 st = 24. The cost of operating the refrigerator accumulates at the rate of $0.001 per hour for each degree that the temperature in the kitchen exceeds the temperature inside the refrigerator. Writ but do not evaluate, an expression involving an integral that can be used to find the cost of operating the refrigerator for the 24-hour interval.