How to obtain an equation for this grapgh?

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SUMMARY

The discussion focuses on deriving an equation for a graph resembling cosine functions with varying amplitudes. A proposed equation format is y = aebxcos(cx), where the coefficients a, b, and c are determined by using coordinates from three points on the graph. Participants emphasize the importance of validating the equation against additional points on the graph to ensure compatibility. This method provides a systematic approach to modeling the graph mathematically.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cosine functions.
  • Familiarity with mathematical modeling and equation derivation.
  • Ability to analyze graph coordinates and extract data points.
  • Basic knowledge of exponential functions and their applications.
NEXT STEPS
  • Learn how to derive equations from graphs using regression analysis.
  • Study the properties of cosine functions and their transformations.
  • Explore techniques for fitting mathematical models to data points.
  • Investigate the use of software tools for graphing and equation fitting, such as Desmos or GeoGebra.
USEFUL FOR

Students in mathematics or engineering fields, educators teaching graphing techniques, and anyone involved in mathematical modeling or data analysis.

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Homework Statement


i am doing my Honor project and i have obtained a graph like the picture below,now i must give an equation for this graph,any ideas how i can obtain an equation which is compatible with this graph?
thanks
 

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i have an idea about this,it seems they are like Cosine functions with different amplitudes,but what can be an equation for it?
 
Possibly. It might, for example, be y= aebxcos(cx). See if you can find a, b, and c by letting x and y be coordinates of three points on your graph. And then, check to see if they work for other points on the graph.
 

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