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I'm first to find the units of all model parameters and subsequently non-dimensionalise the equation. We're given that $y$ and $t$ have units of time whilst $c$ has units of length (with $c$ taken to be a model parameter and $e^x=exp(x)$). The equation is:

$$ y + b{e^{\gamma t}}=c $$

I understand that to begin with I should re-write the two variables $y$ and $t$ as, say:$$y=y^*y'$$$$t=Tt'$$ Beyond this I don't really know what I should do, any help would be appreciated.

Jamie3213
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1 Answers1

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You can't have $y$ a time and $c$ a length unless there is a multiplicative constant to fix that. The units on all terms that are added or subtracted need to be the same.

Ross Millikan
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  • I was thinking the same thing which is why I didn't seem to be getting anywhere, my lecturer had said something along lines of "oh just take $c$ to be anything, say a length" but maybe he was referring to the previous question. Say I take $c$ to have some arbitrary unit, will the question work or does $c$ need to have a pre-defined unit consistent with the equation? – Jamie3213 Feb 26 '14 at 18:19
  • If $y$ is time, then $b$ and $c$ needs to be time as well. They don't have to match $t$. You could also have $y,b,c$ all be length, for example. You need $\gamma$ to have the inverse units of $t$ so the exponential is applied to something dimensionless. Then to make it dimensionless, divide by something of the same unit as $y$ – Ross Millikan Feb 26 '14 at 18:33