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For many natural process of growth, with the growth rate independent of sizedue to Gibrat law and with the growth process following a log-normaldistribution, the ratio between the time (D) for maximum value and the time (L)for maximum growth rate (inflexion point) is then equal to the square root ofthe base of the natural logarithm (e^{1/2}). On the logarithm scale this ratiobecomes one half ((1/2)). It remains an open question, due to lack of completedata for various cases with restricted growth, whether this e^{1/2} ratio canbe stated as e^{1/2}-Law. Two established examples already published, one foran epidemic spreading and one for droplet production, support however thisratio. Another example appears to be the height of humain body. For boys themaximum height occurs near 23 years old while the maximum growth rate is at theage near 14, and there ratio is close to e^{1/2}. The main theoretical base toobtain this conclusion is problem independent, provided the growth process isrestricted, such as public intervention to control the spreading ofcommunicable epidemics, so that an entropy is associated with the process andthe role of dissipation, representing the mechanism of intervention, ismaximized. Under this formulation the principle of maximum rate of entropyproduction is used to make the production process problem independent.

The number e^{(1/2)} is the ratio between the time of maximum value and the time of maximum growth rate for restricted growth phenomena?