Biomedical Statistics and Informatics 2018; 3(3): 43-48 http://www.sciencepublishinggroup.com/j/bsi doi: 10.11648/j.bsi.20180303.11 ISSN: 2578-871X (Print); ISSN: 2578-8728 (Online) Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach Samuel Olukayode Ayinde * , Roseline Bosede Ogunrinde Department of Mathematics, Faculty of Science, Ekiti State University, Ado Ekiti, Nigeria Email address: * Corresponding author To cite this article: Ayinde Samuel Olukayode, Ogunrinde Roseline Bosede. Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach. Biomedical Statistics and Informatics. Vol. 3, No. 3, 2018, pp. 43-48. doi: 10.11648/j.bsi.20180303.11 Received: July 6, 2018; Accepted: August 3, 2018; Published: August 31, 2018 Abstract: A lake is classified as a body of relatively still water that is almost completely surrounded by land with a river or stream that feeds into it or drains from it. A lake that has fish that you can catch can either be man-made or natural, with natural lakes tending to have more successful results. In this research, an interpolating function was proposed following Gompertz function approach considering the scale and shape parameters, a Numerical Method was developed and applied to solve the biological fish lake stocking and growth problem which gives effective results as when Gompertz equation was used directly. Numerical method is an effective tool to solve the problem of growth as its applicable in Gompertz equation. The method results obtained found to be favourable when the Numerical Solution and Analytical Solution is compared as the error obtained is minimal showing the effectiveness of the Method. Gompertz Function or equation was for long of interest only to actuaries and demographics. Its however, recently been used by various authors as a growth curve or function both for biological, economics and Management phenomena. Therefore, we have been able to show how the numerical integration obtained from the interpolating function work the same way Gompertz function worked. Keywords: Gompertz Equation, Mathematical Integration, Logistic Growth, Carrying Capacity 1. Introduction Freshwater Lakes are in very different places, so is the rushing oceans of the world. The creatures that live in them are different to one another in nature, among which is the fish. It is generally known that we have Lake (freshwater) fish and ocean (saltwater) fish. These lakes or oceans have diverse fish population and the growth of a lake or ocean fish depends on the nutrients, minerals and the food available. A fishery is an area with an associated fish or aquatic population, which is harvested for its commercial or recreational value. Fisheries can be wild or farmed with various population dynamics. [1] Population dynamics describe the ways in which a given population grows and shrinks over time, as controlled by birth, death and migration. It is the basis for understanding changing fishery patterns and issues such as habitat destruction, predation and optimal harvesting rates. [2] As a result of acidification, reproduction of fish fails and population densities decrease. The growth of fish is most clearly affected at a late stage of acidification (pH < 5), when the only fish remaining are those in the sparse populations of fish, then few fish have plenty of food, and they can grow remarkably fast. Despite their good tolerance to acidity, small fish may grow slowly. However, if they find something to displace fish food, they are likely to grow normally at least during their early years of life. Though certain kind of whitefish tolerates acidity. The growth of whitefish was faster in lakes without roach than in lakes that had thriving roach populations. The population dynamics of fisheries are used by fisheries scientists to determine sustainable yields, [3, 4] The basic accounting relation for population dynamics is the BIDE (Birth, Immigration, Death, Emigration) model shown as      (1) Where   is the number of individuals at time 1,   is the number of individuals at time 0,  is the number of individuals born,  is the number that died,  is the number