Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach

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.