Functions that exhibit exponential decay behavior?

In summary, the conversation discusses a homework assignment to model a real life system using differential equations, specifically a pendulum. The person is struggling with using an exponential function as the rate of change and is looking for other functions that exhibit the same behavior or considering using a linear approximation.
  • #1
Buffel
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Any help is appreciated, thanks.

Homework Statement


In my course of differentials equations we were given the task to model a real life system with them, we choosed something that resembles a pendulum.

Homework Equations


The Attempt at a Solution


We went to the lab and got experimental data from our system and the resulting data plot looks like a decaying exponential, but using an exponential as our rate of change results in a very complicated system of equations and I was wondering if there exists any other function that exhibits the same behavior or give up and use a linear approximation.
 
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  • #2
Many functions, when multiplied by an exponential function, will look similar. Without more details on your problem, it is hard to suggest anything.
 

Related to Functions that exhibit exponential decay behavior?

1. What is an exponential decay function?

An exponential decay function is a type of mathematical function that represents a decrease in value over time or distance. It is characterized by a constant base raised to a negative power, such as y = ab^-x.

2. What are some real-life examples of exponential decay functions?

Examples of exponential decay functions can be found in various natural phenomena, such as radioactive decay, population growth, and the decay of electrical signals in circuits. It can also be observed in financial trends, such as compound interest and stock market fluctuations.

3. How is an exponential decay function different from an exponential growth function?

An exponential decay function has a negative exponent, while an exponential growth function has a positive exponent. This means that an exponential decay function decreases in value over time or distance, while an exponential growth function increases in value.

4. What is the relationship between the base of an exponential decay function and its rate of change?

The base of an exponential decay function determines the rate of change. A base less than 1 will result in a slower decay, while a base greater than 1 will result in a faster decay. This can be seen in the graph of the function, where a steeper curve indicates a faster rate of decay.

5. How can we model an exponential decay function mathematically?

An exponential decay function can be modeled using the general form y = ab^-x, where 'a' is the initial value and 'b' is the decay factor. Alternatively, it can also be expressed as y = y0e^-kx, where 'y0' is the initial value and 'k' is the decay constant. Both equations can be used to calculate the value of the function at a specific time or distance.

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