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- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/02%3A_Applications_of_First_Order_EquationsThis page covers applications of first-order differential equations, focusing on exponential growth and decay, including radioactive decay, carbon dating, and compound interest. It discusses complex g...This page covers applications of first-order differential equations, focusing on exponential growth and decay, including radioactive decay, carbon dating, and compound interest. It discusses complex growth scenarios, Newton's law of cooling, motion in resistive media, and mixing problems. Additionally, it introduces orthogonal trajectories and pursuit curves, alongside exercises for practical comprehension.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/02%3A_Applications_of_First_Order_Equations/2.01%3A_Growth_and_Decay/2.1E%3A_Exercises_for_Section_2.1This page presents a collection of exercises on growth and decay models using differential equations, covering topics like radioactive decay, financial growth, and production rates. It challenges read...This page presents a collection of exercises on growth and decay models using differential equations, covering topics like radioactive decay, financial growth, and production rates. It challenges readers to find quantities over time based on initial conditions, express decay constants, and solve equations related to various scenarios such as substance decay, bank account management, and product manufacturing.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.06%3A_Dynamical_Systems/6.6E%3A_Exercises_for_Section_6.6This page provides exercises on modeling predator-prey populations, specifically focusing on coyotes and rabbits using dynamical systems and matrices. It includes calculations of populations for speci...This page provides exercises on modeling predator-prey populations, specifically focusing on coyotes and rabbits using dynamical systems and matrices. It includes calculations of populations for specific months, matrix diagonalization, and long-term behavior analysis. Similar examples with foxes and mice, and hawks and squirrels, explore population dynamics. The goal is to analyze and predict trends based on initial conditions and species interactions.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.09%3A_Derivatives_of_Exponential_and_Logarithmic_Functions/3.9E%3A_Exercises_for_Section_3.10This page focuses on exercises for finding derivatives of various mathematical functions, emphasizing techniques like logarithmic differentiation and their real-life applications, including population...This page focuses on exercises for finding derivatives of various mathematical functions, emphasizing techniques like logarithmic differentiation and their real-life applications, including population growth and decay modeling. It features the Gompertz growth function with historical NYC population data (1790-1860), detailing the relative rate of change and fitting an exponential curve. A derived model \(p=35741(1.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.08%3A_Exponential_Growth_and_DecayOne of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and con...One of the most prevalent applications of exponential functions involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications.
