Mathematical modeling | Growth curves | Ordinary differential equations | Temporal exponentials
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression. The formula for exponential growth of a variable x at the growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is where x0 is the value of x at time 0. The growth of a bacterial colony is often used to illustrate it. One bacterium splits itself into two, each of which splits itself resulting in four, then eight, 16, 32, and so on. The amount of increase keeps increasing because it is proportional to the ever-increasing number of bacteria. Growth like this is observed in real-life activity or phenomena, such as the spread of virus infection, the growth of debt due to compound interest, and the spread of viral videos. In real cases, initial exponential growth often does not last forever, instead slowing down eventually due to upper limits caused by external factors and turning into logistic growth. Terms like "exponential growth" are sometimes incorrectly interpreted as "rapid growth". Indeed, something that grows exponentially can in fact be growing slowly at first. (Wikipedia).
Follow updates on Twitter: https://twitter.com/eigensteve This series discusses exponential growth, which is a ubiquitous phenomenon in science and engineering. This video will provide a high-level overview. Website: https://www.eigensteve.com/
From playlist Intro to Data Science
Introduces notation and formulas for exponential growth models, with solutions to guided problems.
From playlist Discrete Math
Exponential Growth Models - Part 2 of 2
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From playlist Exponential and Logarithmic Expressions and Equations
Follow updates on Twitter: https://twitter.com/eigensteve This video discusses how all exponential growth eventually tapers off, through one mechanism or another. Website: https://www.eigensteve.com/
From playlist Intro to Data Science
Exponential Growth Models - Part 1 of 2
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From playlist Exponential and Logarithmic Expressions and Equations
Exponential Function Application (y=ab^x) - Population Growth of India
This video provide an example of how an exponential function can be found to determine population. The function is then used to make a prediction about the population in the future. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Solving Applications of Exponential Growth and Decay
Ex: Exponential Growth Application - Predicting World Population
This video provides an example of how to write exponential function and make a prediction about population when given the population of a given year with the annual growth rate. http:/mathispower4u.com
From playlist Solving Applications of Exponential Growth and Decay
Introduction to Exponential Functions in the Form f(x)=ab^x - Part 1
This video introduces exponential growth and exponential decay functions in the form y=ab^x. http://mathispower4u.com
From playlist Introduction to Exponential Functions
Exponential Growth: Recursive and Explicit Equations Part 2
This video explains how to express exponential growth using recursive and explicit equations. Site: http://mathispower4u.com
From playlist Linear, Exponential, and Logistic Growth: Recursive/Explicit
Hyperexponential Growth and Log-periodicity Precede Extreme COVID-19 Waves by Induja Pavithran
PROGRAM TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID) ORGANIZERS: Partha Sharathi Dutta (IIT Ropar, India), Vishwesha Guttal (IISc, India), Mohit Kumar Jolly (IISc, India) and Sudipta Kumar Sinha (IIT Ropar, India) DATE: 19 September 2022 to 30 September 2022 VENUE: Ramanujan Lecture Hall an
From playlist TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID, 2022)
Compare Linear and Exponential Growth Using Recursive and Explicit Equations
This video explains the different between linear and exponential growth. Both recursive and explicit equations are discussed. Site: http://mathispower4u.com
From playlist Linear, Exponential, and Logistic Growth: Recursive/Explicit
Ex: Identify the Initial Value and Exponential Growth or Decay Rate Given an Exponential Function
This video explains how to find the exponential growth or decay rate and the initial value given an exponential function in the form y=ab^x. Site: http://mathispower4u.com
From playlist Solving Applications of Exponential Growth and Decay
Camille Horbez: Automorphisms of hyperbolic groups and growth
Abstract: Let G be a torsion-free hyperbolic group, let S be a finite generating set of G, and let f be an automorphism of G. We want to understand the possible growth types for the word length of fn(g), where g is an element of G. Growth was completely described by Thurston when G is the
From playlist Topology
Laurent Bartholdi - Imbeddings in groups of subexponential growth
Laurent Bartholdi (University of Gottingen, Germany) A finitely generated group has subexponential growth if the number of group elements expressible as words of length $\le n$ grows subexponentially in $n$. I will show that every countable group that does not contain a subgroup of expone
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Examples of Exponential Growth
Follow updates on Twitter: https://twitter.com/eigensteve This video will go through some of the many examples of exponential growth in science and engineering. Website: https://www.eigensteve.com/
From playlist Intro to Data Science
How To Tell If We're Beating COVID-19
This video made possible with support of Brilliant - the first 200 subscribers to go to http://Brilliant.org/MinutePhysics get 20% off a Premium subscription to Brilliant. Go to http://aatishb.com/covidtrends to explore the graph from the video yourself! RESOURCES Grant's 3Blue1Brown Vid
From playlist MinutePhysics
Exponential Growth and its Philosophical Implications
Economists use exponential functions to model economic growth. The human population is presently growing exponentially. However, any exponential growth that continues indefinitely would eventually expand faster than the speed of light, in direct violation of the known laws of physics. M
From playlist Physics
Introduction to Exponential Equations in Two Variables
This video introduces linear equations in the form y=a(b)^x. http://mathispower4u.com
From playlist Introduction to Exponential Functions