Question

The rate at which a battery charges is slower the closer the battery is to its maximum charge C0. The time (in hours) required to charge a fully discharged battery to a charge C is given by an equation i'll post as a comment on this in just a sec...

where k is a positive constant that depends on the battery. For a certain battery, k = 0.35. If this battery is fully discharged, how long will it take to charge to 70% of its maximum charge C0? (Round your answer to three decimal places.)

Answer 1

\[t= -k \ln (1-\frac{ C }{ C _{o} })\]

Answer 2

What did you get?

Answer 3

I was wondering if the equation once the numbers are plugged in would be \[t=-.35\ln(1-\frac{ 100 }{70})\]?

Answer 4

it's 70/100, not 100/70

Answer 5

\[C /C _{0}=.7\]
ln(1-.7)=-1.20397

t=-k*-1.20397
=-.35*-1.20397
=.42139
~=.421 seconds

Answer 6

t=.421?

Answer 7

Approximately, yes. Do you understand why?

Answer 8

yeah i figured it out!

Answer 9

:)