What is the 1/e Lifetime of a Graph?

[Richard Ros]

Homework Statement

Given that... The units of voltage are “Volts” and the units of time are “seconds”
Show τe (1/e life-time) on your graph and find a value for τe from your graph. ( The definition of τe is similar to the definition of τ1/2 (half-life))

V(t) t(s)
24 0.1
20 0.2
14 0.3
12 0.4
10 0.5
7.5 0.6
5.5 0.7
4.8 0.8
3.5 0.9
2.6 1.0

Homework Equations

V(t) = Vi*e^-αt

The Attempt at a Solution

I got the half life as .3 seconds. But I have no idea what is the life-time of a graph and how to even get it. I've tried googling it but to no avail. If anyone can help tell me the value and how you got it, I would greatly appreciate it. Thanks!

 

[Chestermiller]

Homework Statement

Given that... The units of voltage are “Volts” and the units of time are “seconds”
Show τe (1/e life-time) on your graph and find a value for τe from your graph. ( The definition of τe is similar to the definition of τ1/2 (half-life))

V(t) t(s)
24 0.1
20 0.2
14 0.3
12 0.4
10 0.5
7.5 0.6
5.5 0.7
4.8 0.8
3.5 0.9
2.6 1.0

Homework Equations

V(t) = Vi*e^-αt

The Attempt at a Solution

I got the half life as .3 seconds. But I have no idea what is the life-time of a graph and how to even get it. I've tried googling it but to no avail. If anyone can help tell me the value and how you got it, I would greatly appreciate it. Thanks!

The 1/e lifetime is 1/α. Take the natural log of both sides of the equation. Graph the data using a semi-log scale for V and an arithmetic scale for t. The slope should be -α. See if you can figure out why this procedure works.