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Problem - Power and Energy
The total energy in megawatt-hr (MWh) used by a town is given by
E(t) = 400t + (2400/π)sin(πt/12),
Where t ≥ 0 is measured in hours, with t = 0 corresponding to noon.
a) Find the power, or rate of energy consumption, P(t) = E'(t) in units of megawatts (MW).
b) At what time of day is the rate of energy consumption a maximum? What is the power at that time of day?
c) At what time of day is the rate of energy consumption a minimum? What is the power at that time of day?
d) Sketch a graph of the power function reflecting the times when energy use is a minimum or a maximum.
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