physics prob yuck!?

Question

Given t1/2 to be 0.0133 seconds, how long should it take to reach 87.5% of maximum charge?
time = _________________seconds.
(Answer with three significant figures or N/A if there is no answer.)

please help and explain how to do this, thanks

Answer 1

This one is set up to be simple. In each half time t(1/2) the difference between charge and max charge decreases to 0.5 * its previous value. At 87.5% it has decreased to within 0.125 of the max. This takes 3 half times (0.5, 0.25, 0.125), or 0.04 s.
In general the number of half times = ln(1-final value)/ln(0.5). In this problem, 1-final value = 0.125.