problem involving the number e

[jonnburton]

Hi,

I was wondering whether someone could help me with this problem:

The current,I amps, flowing through an electric circuit at time t seconds after closing the switch is given by \(\displaystyle I = 2e^{-\frac{t}{5}}\)

I have to determine the time in seconds for the current to decrease to 0.4 amps.

In principle I know what should be done, rearrange the equation to make t the subject. But I'm not sure how to do this. I know that \(\displaystyle N = e^x \Leftrightarrow x = ln N\).

However, the 2 in front of the 'e' is throwing me; I'm not sure how to deal with this.

If anyone could explain what to do I would be very grateful.

 

[MarkFL]

Set \(\displaystyle I=0.4\) then divide through by 2 first, then convert to logarithmic form.

 

[jonnburton]

Set \(\displaystyle I=0.4\) then divide through by 2 first, then convert to logarithmic form.

Thanks a lot MarkFL, I will try that.