Capacitor Discharge: Calculating Rate of Voltage Change and Time

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Homework Statement


When a condenser discharges electricity, the instantaneous rate of change of the voltage is proportional to the voltage in the condenser.
Suppose you have a discharging condenser and the instantaneous rate of change of the voltage is 1/100 of the voltage (in volts per second). How many seconds does it take for the voltage to decrease by 90%?


Homework Equations



e^-rt

The Attempt at a Solution

Log 90= e^-t ? = 4.49?
 
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It's wrong. Try to give a more detailed calculation and explain what it is you do.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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