If the rate at which a battery charges is slower the closer the battery is to its maximum charge C0, then the time (in hours) required to charge a fully discharged battery to a charge C is given by
t=−kln(1−CC0)
where k is a positive constant that depends on the battery. For a certain battery, k=0.25. Suppose this battery is fully discharged, how long will it take to charge to 90% of its maximum charge C0?
If charge C is 90% of charge C0, then
C=0.9C0
So,
t=−kln(1−0.9\cancelC0\cancelC0)Substitute C=0.9C0t=−0.25ln(1−0.9)Simplifyt=0.58 hours
This means that it will take 0.58 hours to charge to 90% of its maximum charge C0.
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