The article solves the problem of finding the maximum number of solutions for equations composed of power functions and sums of exponential functions. It introduces concept of corresponding functions and proves the relationships between the properties of polynomial, power and sums of exponential functions. One of the results is generalization of Descartes Rule of Signs for other than polynomial functions. Obtained results are applied to two practical problems. One is the finding of an adequate description of transition electrical signals. Secondly, the proved theorems are applied to the problem of finding the initial value for iterative algorithms used to solve one particular case of IRR (internal rate of return) equation for mortgage calculations. Overall, the results are proved to be beneficial for theoretical and practical applications in industry and in different areas of science and technology.
polynomials Descartes rule of signs, power function exponential function logarithmic functions real solutions corresponding equations, transition process, IRR equation