From the course: Complete Guide to Differential Equations Foundations for Data Science
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Growth and decay
From the course: Complete Guide to Differential Equations Foundations for Data Science
Growth and decay
- [Instructor] In this chapter, you will explore multiple applications for first order differential equations. These types of equations tend to have the most amount of practical applications compared to the other orders. This is why I will focus on a variety of their applications for a whole chapter instead of just one video. In this chapter, you will explore growth and decay, population, orthogonal trajectories, velocity, cooling and heating, mixing, carbon-14 dating, RC circuits, and curves. Let's start off by exploring growth and decay. Growth and decay describes systems where the rate of change of a quantity is proportional to the quantity itself. Note that this is sometimes referred to as exponential growth and decay. You will use this general concept in many of the following applications. Note that growth is when the rate of change is in a positive direction, and decay is when the rate of change is in a negative direction. The general formula for growth and decay is dy dt equals…
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