Determination parameter of exponential function based positive number

Abstract

Abstract The relationship between variables can be made a model or function. The use of the function is as a tool for making a prediction of the response, provided the value of the predictor is known. A function has independent variable, dependent variable, and parameter. The function discussed is an exponential function with base number in positive number. Furthermore, it is developed in the form of the exponential function with one parameter, the exponential function with two parameters and the exponential regression model. To create a function required some parameters. We need a certain method to find parameter. The accuracy of obtained function model shows the goodness of the function in approaching the distribution of the data. The method used to find parameter using the sum square error and logarithm function. Using logarithm function produces a linear function. Computation of parameters using R and Matlab programs. To measure the value of model accuracy using the mean square error. The purpose of this study is to find parameter of the exponential function with one parameter, the exponential function with two parameters and the exponential regression model. The presentation of the result of this discussion is in form of table and picture in the hope that it is easy to understand and interesting. The output of the exponential function with one parameter shows that the base value is 1.050021, the parameter value α is 7.969737 and the prediction accuracy value is 99.996%. The exponential function with two parameters shows that the base value is 0.5, the parameter value α is 7.969737, and the parameter value β is - 0.071, while for the base value is 10, the parameter value α is 7.969737, and the parameter value β is 0.02. The prediction accuracy of the exponential function with two parameters is 99.996%. While the exponential regression model shows that the base value is 0.5, the parameter value α is 128.336, and the parameter value β is -55.828. The prediction accuracy of the exponential regression model is 84.8%.