Data from an experiment may result in a graph indicating exponential growth. This implies the formula of this growth is \(y = k{x^n}\), where \(k\) and \(n\) are constants. Using logarithms, we can ...

Exponential and logarithmic equations are fundamental in mathematics, crucial for understanding growth patterns, decay processes, and solving complex problems. This video provides a clear and ...

Remember one of the laws of logs: \(n{\log _a}x = {\log _a}{x^2}\) Another one of the laws are used here: \({\log _a}x + {\log _a}y = {\log _a}xy\) ...

Concepts covered in this course include: standard functions and their graphs, limits, continuity, tangents, derivatives, the definite integral, and the fundamental theorem of calculus. Formulas for ...

What are the underlying principles of how populations change over time? Two basic principles are involved, the idea of exponential growth and its ultimate control. The basics of population ecology ...

In this article, we prove an inequality between the ratio of the extended logarithmic means and the ratio of the exponential means. The proof is based on an inequality between logarithmic mean and one ...

Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

A system of linear ordinary differential equations with exponential coefficients is considered; several theorems are presented concerning general solutions and their asymptotic forms for large values ...