Development of a Mathematical Model to Calculate Accumulated Solid Waste: An Experiments and Statistical Sampling.


 In newest development, waste is being refined into a biofuel or recycled. Waste management has being an important factor in community development. The transformation of waste into useful materials has received much work. Therefore, database must be developed to know the amount of waste accumulated or generated over a given period of time. Taken into consideration the burning and recycle reduction factor, incremental factor and degradable waste ratio. This paper look for a mathematical formula that can be used to generate data for amount of solid waste accumulated over time for geographical location in respect of mass.


Abstract
In newest development, waste is being refined into a biofuel or recycled. Waste management has being an important factor in community development. The transformation of waste into useful materials has received much work. Therefore, database must be developed to know the amount of waste accumulated or generated over a given period of time. Taken into consideration the burning and recycle reduction factor, incremental factor and degradable waste ratio. This paper look for a mathematical formula that can be used to generate data for amount of solid waste accumulated over time for geographical location in respect of mass.
Keywords: Waste management, solid waste collection, data collation, mathematical model

Introduction
Estimation has been given of waste generated in a geographical location per day (Alare, 2020). The formula works with the estimated figures of waste generated per day geographical location using statistical models sampling (Castle, 1993).
The importance of data in this present age cannot be overemphasized. It is important because it provide useful information for institutions, organizations and researchers of past record.
The aim of this research is to develop a formula that will help companies, institutions and researcher of biofuel, bioenergy system and other waste transformation related fields determine the amount of solid waste available to them in a geographical location based on the data derived from the formula and waste chart.

Methods
To determine the estimated accumulated waste of a geographical location for a given time interval. Three factors were considered and these factors varies from different geographical locations. Therefore, geographical locations should be experimental samples. The factors are: Waste incremental ratio (i) Degradable waste ratio (c) Burning and recycle reduction factors These factors tend reduce or increase the accumulated waste from expected waste generated. The availability of waste to waste companies can be examined using these factors. To determine these factors, statistical model and experimental sample methods will be employed. (Dass, 2008) t is number of days used which is kmax

2. Average waste incremental ratio
In order to avoid or minimize mathematical and computational error, a small number of samples and minimum duration of days is advice.

Experimental Method Procedure
Create space samples of dumpsite A,B,C,D,E,……….∞ in a closed and isolated system The assumed burning factor is in the range of 0.005 to 0.006 depending on the burning and recycling activities of the geographical area considered.

Result
A reduction constant k is developed from the mathematical combination of all the factors ensuring that reduction is at a reasonable range.
The amount of solid waste accumulated over a given period in term of the mass is given as Where M is accumulated waste over a period of time K is reduction constant T0 is period of time taken in days

0 Conclusion
This paper has shown a method of calculating the amount of accumulated solid waste in mass. The factors consider varies from one geographical area to another. We employ researchers to further the research. with the aim of obtaining the factors for different geographical locations in the world. Develop a chart that will contain the data of all i, c and k for all experimented geographical area.