Power and energy? Energy is the capacity to do work and power is the rate at which energy is used or consumed. Therefore, if ?E?(?t?) is the energy function for a system, then ?P?(?t?) = ?E??(?t?) is the power function. A unit of energy is the kilowatt-hour (1 kWh is the amount of energy needed to light ten 100-W light bulbs for an hour); the corresponding units for power are kW. The following figure shows the energy consumed by a small community over a 25-hr period. a.? Estimate the power at ?t? = 10 and ?t? = 20 hr. Be sure to include units in your calculation. b.? At what limes on the interval [0, 25] is the power zero? c.? At what times on the interval [0, 25] is the power a maximum?

SOLUTION STEP 1 Given energy = E(t). d Then power P(t) = dtE(t) = E(t) Given, A unit of energy is the kilowatt-hour (1 kWh is the amount of energy needed to light ten 100-W light bulbs for an hour); the corresponding units for power are kW. The following figure shows the energy consumed by a small community over a 25-hr period. STEP 2 An estimated graph of its derivative can be drawn as follows(ie,...