The electrical potential in a circuit is given by V(t)= 320e^-3.1t, where t is measured in seconds and V is measured in volts. How long does it take for the potential to drop from 200 volts to 100 volts?

Question

mathmale · Answer

One possible approach would be to calculate the time at which the original 320 volt electric potential reached 200 volts, and then calculate the time at which the original 320 volts decreased to 100 volts, and then subtract the two times.

mathmale · Answer

Although I won't provide the "exact" answer, it's approx. 1/4 sec., if I've done my calculations correctly.

If you'd care to show some work, I'd be happy to give you feedback and guidance.

anonymous · Answer

So I've found V(200)= .152 and V(100) = .375. If I've done my math correctly and I've subtracted my two answers and I get .223 but maybe I'm doing something wrong because it is not the correct answer.

mathmale · Answer

actually, you've done precisely what I did.  My answer was .224, after rounding it up from .2236.  Does that help?

anonymous · Answer

YES!!! that helps! I just rounded wrong! Thank you so much!

mathmale · Answer

My great pleasure.  This is not the easiest of problems, so your obtaining the correct result says a lot of good about you.

anonymous · Answer

Thanks! I have one more question if at some instant in time the voltage is V(t)= X volts.. How long will it take for the potential to drop to 0.5X volts. How do I approach this question?