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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.
Exponential growth happens when an initial population increases by the same percentage or factor over equal time increments or generations. This is known as relative growth and is usually expressed as percentage. For example, let’s say a population is growing by 1.6% each year.
Lesson 1: Exponential vs. linear growth. Intro to exponential functions. Exponential vs. linear growth. Warmup: exponential vs. linear growth. Exponential vs. linear growth. Exponential vs. linear models: verbal. Exponential vs. linear models: table.
Using Exponential Functions to Model Growth and Decay. In exponential growth, the value of the dependent variable \(y\) increases at a constant percentage rate as the value of the independent variable (\(x\) or \(t\)) increases. Examples of exponential growth functions include:
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. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature.
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).
Common examples of exponential growth in real-life scenarios include the growth of cells, the returns from compounding interest from an investment, and the spread of a disease during a pandemic.
Use the exponential growth model in applications, including population growth and compound interest; Explain the concept of doubling time
Examples of Exponential Growth 1. Spread of Virus. The spread of a virus generally follows exponential growth. This can best be observed by looking at the spread of a viral disease.
What do you notice? What do you wonder? What impact does this have on you and your community? What’s going on in this graph? Write a headline that captures the graph’s main idea. Math Activity #1:...