Exponential Growth And Decay Notes PdfBy Dielle B. In and pdf 19.05.2021 at 06:13 6 min read
File Name: exponential growth and decay notes .zip
Exponential growth & decay word problems
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The base, b , is constant and the exponent, x , is a variable. Rate of Change: This graph does not have a constant rate of change, but it has constant ratios. It is growing by common factors over equal intervals. We have seen that exponential functions grow by common factors over equal intervals. As such, exponential functions are used to model a wide range of real-life situations such as populations, bacteria, radioactive substances, temperatures, bank accounts, credit payments, compound interest, electricity, medicine, tournaments, etc.
Exponential growth and decay
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 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.
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. In this section, we examine exponential growth and decay in the context of some of these applications. Many systems exhibit exponential growth. Notice that in an exponential growth model, we have. That is, the rate of growth is proportional to the current function value. This is a key feature of exponential growth.
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