Tuesday, September 23, 2014

College Algebra, Chapter 5, 5.2, Section 5.2, Problem 86

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(1CC0)

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(10.9\cancelC0\cancelC0)Substitute C=0.9C0t=0.25ln(10.9)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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