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Determine how long an energy storage device can be used when it is known that for...

Determine how long an energy storage device can be used when it is known that for this type of system the output power is a polynomial function of time, (Power) = a0 - bt 2 , where a0 = 2.5(105 ) W and b = 1.24(10-3 ) W/s 2 are known constants and t is the time in seconds. The initial energy stored in the device at the start of this process is 8.1(108 ) J and the device is completely discharged at the end of the process.

Please solve with sketches and clear equations. Thanks!

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