How to deal with the size of the exponential type function's argument?

I have the following function in a report of global size 12 :

$Q= \rho V c_{p} \left( T -T_{\infty} \right) [ 1-e^{\frac {h A_s}{\rho V c_{p}}t}]$


As one would expect, the exponential function's argument appears very tiny:

Now , my question is that:

Are there ways to make deal with this problem?Some people may suggest and have suggested) that I change the argument's font size..that surely is a way but in small font sizes such as font size 12, it looks terrible , and others suggest to use the exp function , but I feel that , that answer applies to a class of functions that have popular inline alternatives.

Also answers suggested should be within the range of good scientific/mathematical documentation practices.

• Welcome to TeX.SX! You may have a look on our starter guide. – jub0bs May 20 '13 at 14:20
• I wouldn't use superscripts in this case, I would use the \exp notation: $Q= \rho V c_{p} ( T -T_{\infty} )\Bigl[ 1-\exp\Bigl({\frac {h A_s}{\rho V c_{p}}t\Bigr)}\Bigr]$. Perhaps it would also be a good idea to use a displayed expresion. – Gonzalo Medina May 20 '13 at 14:22
• noted the the point raised in your answer , but how is that any different from what the answer mentioned below..i.e in your answer you scaled the superscript , in the answer mentioned below he scaled the font of the superscript ? – metric-space May 20 '13 at 15:25

I would suggest:

$Q= \rho V c_{p} \left( T -T_{\infty} \right) [ 1-e^{h A_s t / \rho V c_{p}}]$


or, if you really want the t kept separate from the fraction, then:

$Q= \rho V c_{p} \left( T -T_{\infty} \right) [ 1-e^{(h A_s / \rho V c_{p})t}]$


Results:

A number of possibilities to choose from:

\documentclass{article}
\usepackage{graphicx}
\usepackage{amsmath}

\begin{document}
\noindent Inline math:\\

$Q= \rho V c_{p} ( T -T_{\infty} ) [ 1-e^{\frac {h A_s}{\rho V c_{p}}t}]$

$Q= \rho V c_{p} ( T -T_{\infty} ) \Bigl[ 1 - e^{\scalebox{1.2}{$\frac {h A_s}{\rho V c_{p}}t$}} \Bigr]$

$Q= \rho V c_{p} ( T -T_{\infty} ) \Bigl[ 1 - \exp\Bigl({\frac {h A_s}{\rho V c_{p}}t\Bigr)}\Bigr]$
\quad (better)\$1em] \noindent Display math: \[ Q= \rho V c_{p} \left( T -T_{\infty} \right) \left[ 1-\exp{\left( \frac {h A_s}{\rho V c_{p}} t \right)} \right] \quad \text{(much better)}$
\end{document}

• I was wondering if your answer would the same if rather than using the exponential function , you were using lets say some other function that did not have a recognized inline type alternative(all the other above restrictions are in place)? – metric-space May 20 '13 at 14:53
• @nerorevenge Suppose for the sake of argument e was \theta then I guess the only possibility is using a few \fractions next to each other in the exponent such that, at least, the readability is preserved as much as possible. – percusse May 20 '13 at 15:18

$Q= \alpha \Delta T \left( 1-e^{\beta t}\right)$,

where $\alpha=\rho V c_{p}$,
$\Delta T=T-T_{\infty}$,
$\beta=h A_s / \alpha$.