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# Proving an exponential relationship watch

1. Physics A2
I know how to prove that something is exponential with regards to time (graph of natural log whatever against time gives a negative gradient with +ve y intercept. I have only ever seen these exponential relationships with time and the notes my teacher gave just say "to prove something is exponential take logs of values". If time is not a variable do you still end up with a graph of natural log whatever against the other variable or do you take logs of both variables?

Thank you!
2. (Original post by Orangemonkey1)
If time is not a variable do you still end up with a graph of natural log whatever against the other variable
Yes, you do.
3. (Original post by Zacken)
Yes, you do.
Thank you!
4. (Original post by Orangemonkey1)
Thank you!
No problem! I've moved this to the Physics forum for you; in the future, try and post physics related question here. You'll get more attention quicker!
5. (Original post by Orangemonkey1)
Physics A2
I know how to prove that something is exponential with regards to time (graph of natural log whatever against time gives a negative gradient with +ve y intercept. I have only ever seen these exponential relationships with time and the notes my teacher gave just say "to prove something is exponential take logs of values". If time is not a variable do you still end up with a graph of natural log whatever against the other variable or do you take logs of both variables?

Thank you!
Just be careful because that negative part proves exponential decay. The gradient could be positive if it were an exponential growth (e.g. in a capacitor charging up)

Also as a quick tip, remember that in physics, the units for log(dimension) are the same as the units of the actual dimension. I know it seems weird but for example ln(time), where time is measured in seconds, would still be measured in seconds. You must remember this when labelling graphs!
6. (Original post by Student403)
Just be careful because that negative part proves exponential decay. The gradient could be positive if it were an exponential growth (e.g. in a capacitor charging up)

Also as a quick tip, remember that in physics, the units for log(dimension) are the same as the units of the actual dimension. I know it seems weird but for example ln(time), where time is measured in seconds, would still be measured in seconds. You must remember this when labelling graphs!
So it's not In(seconds) ???
7. (Original post by Kyx)
So it's not In(seconds) ???
Nope.

Unit is seconds
8. (Original post by Student403)
Nope.

Unit is seconds
Why?

I mean, time^2 is measured in seconds^2 ... ???
9. (Original post by Kyx)
Why?

I mean, time^2 is measured in seconds^2 ... ???
Yes because that's [time] * [time]. Ln is a function
10. (Original post by Student403)
Yes because that's [time] * [time]. Ln is a function
Oh

and is it L n or I n?

y'know as in 'in'

do you say 'in 3'???
11. (Original post by Kyx)
Oh

and is it L n or I n?

y'know as in 'in'

do you say 'in 3'???
Lower case L.

Can be pronounced "lun" or "L.N.", however you want to.
12. (Original post by Student403)
Lower case L.

Can be pronounced "lun" or "L.N.", however you want to.
So when I wrote 'in' on my ISA, I am going to lose a mark?
13. (Original post by Kyx)
So when I wrote 'in' on my ISA, I am going to lose a mark?
14. (Original post by Student403)
No, I did capital I withn lines at the top and bottom
15. (Original post by Kyx)
No, I did capital I withn lines at the top and bottom
That'll be fine. It's how some people draw their lower case Ls anyway
Spoiler:
Show
And even if you wrote in, I doubt you'd be penalised. Your pencil/pen might have slipped for all they know
16. (Original post by Student403)
That'll be fine. It's how some people draw their lower case Ls anyway
Spoiler:
Show
And even if you wrote in, I doubt you'd be penalised. Your pencil/pen might have slipped for all they know

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