Understanding Exponential Growth in Various Fields
This section explores exponential growth applications across multiple disciplines including physics, chemistry, biology, geology, psychology, and economics. Key examples of exponential growth can be seen in population dynamics, nuclear reactions, chemical reactions, and mental growth. The mathematical foundation is provided through the differential equation dy/dt = k.y, whose solutions demonstrate how quantities grow proportionally to their size. Additionally, practical exercises and examples are available to illustrate these principles in real-world contexts.
Understanding Exponential Growth in Various Fields
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Presentation Transcript
Math 1304 Calculus I 3.8 – Exponential Growth
Applications: Things that grow proportional to their size • Physics • Some nuclear reactions (explosions) • Chemistry • Some chemical reactions (explosions) • Biology • Populations (people, animals, plants) • Individuals (size) • Geology • Some pressure, force, heat • Psychology • Mental growth, … • Economics • Some cost, production volume, profit, overhead • Compound interest
Differential Equation • For the equation: dy/dt = k y • Solution (Th 2 on page 234) The only solutions are y(t) = y(0) e kt
Exercises • See examples and problems in section 3.8.
