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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.
- 4.2 Linear Approximations and Differentials
Analysis. Using a calculator, the value of 9.1 9.1 to four...
- 5.6 Integrals Involving Exponential and Logarithmic Functions
As mentioned at the beginning of this section, exponential...
- 3.9 Derivatives of Exponential and Logarithmic Functions
One model for population growth is a Gompertz growth...
- 6.2 Determining Volumes by Slicing
6.8 Exponential Growth and Decay; 6.9 Calculus of the...
- 6.4 Arc Length of a Curve and Surface Area
Arc Length of the Curve x = g(y). We have just seen how to...
- Introduction
We provide examples of equations with terms involving these...
- Key Terms
This free textbook is an OpenStax resource written to...
- Key Equations
This free textbook is an OpenStax resource written to...
- 4.2 Linear Approximations and Differentials
17 sie 2024 · Exponential growth and exponential decay are two of the most common applications of exponential functions. Systems that exhibit exponential growth follow a model of the form \(y=y_0e^{kt}\). In exponential growth, the rate of growth is proportional to the quantity present. In other words, \(y′=ky\).
Example: Atmospheric pressure (the pressure of air around you) decreases as you go higher. It decreases about 12% for every 1000 m: an exponential decay. The pressure at sea level is about 1013 hPa (depending on weather). Write the formula (with its "k" value),
Describe the relative growth rates of functions. Suppose the functions [latex]f [/latex] and [latex]g [/latex] both approach infinity as [latex]x\to \infty [/latex].
Exponential growth and exponential decay are two of the most common applications of exponential functions. Systems that exhibit exponential growth follow a model of the form [latex]y= {y}_ {0} {e}^ {kt}. [/latex] In exponential growth, the rate of growth is proportional to the quantity present.
Continuous growth can be calculated using the formula [latex]f(x)=ae^{rx},[/latex] where [latex]a[/latex] is the starting amount and [latex]r[/latex] is the continuous growth rate.
The rate is symbolized as dN/dt which simply means “change in N relative to change in t,” and if you recall your basic calculus, we can find the rate of growth by differentiating Equation 4 ...
