The growth process of a living organism is studied with the help of a mathematical model where a part of the surplus power is assumed to be used for growth. In the present study, the basic mathematical framework of the growth process is based on a pioneering theory proposed by von Bertalanffy and his work is the main intellectual driving force behind the present analysis. Considering the existence of an optimum size for which the surplus power becomes maximum, it has been found that the scaling exponent for the intake rate must be smaller than the exponent for the metabolic cost. A relationship among the empirical constants in allometric scaling has also been established on the basis of the fact that an organism never ceases to generate surplus energy. The growth process is found to continue forever, although with a decreasing rate. Beyond the optimum point the percentage of shortfall in energy has been calculated and its dependence on scaling exponents has been determined. The dependence of optimum mass on the empirical constants has been shown graphically. The functional dependence of mass variation on time has been obtained by solving a differential equation based on the concept of surplus energy. The dependence of the growth process on scaling exponent and empirical constants has been shown graphically.

中文翻译：

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缩放指数和其他参数在生长机制中的重要性：一种分析方法。

在数学模型的帮助下研究生物体的生长过程，其中假设一部分剩余功率用于生长。在本研究中，生长过程的基本数学框架基于 von Bertalanffy 提出的开创性理论，他的工作是本分析背后的主要智力驱动力。考虑到剩余功率最大的最佳尺寸的存在，已经发现摄入率的缩放指数必须小于代谢成本的指数。异速生长中的经验常数之间的关系也建立在生物体永远不会停止产生多余能量的事实的基础上。发现增长过程将永远持续下去，尽管速度在下降。在最佳点之外，已经计算了能量短缺的百分比，并且已经确定了它对标度指数的依赖性。最佳质量对经验常数的依赖性已以图形方式显示。通过求解基于剩余能量概念的微分方程，获得了质量变化对时间的函数依赖性。增长过程对标度指数和经验常数的依赖性已以图形方式显示。