Converting Exponential Decay to Polynomial: Solving for Y(0) and k

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Homework Help Overview

The discussion revolves around converting the exponential decay equation y = y(0) * e^(-kt) into a polynomial form. Participants are exploring the implications of this transformation and the associated parameters, particularly focusing on the variable k.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of Taylor series for approximating the exponential function with polynomials, while questioning whether other methods exist. There is also a focus on the nature of the polynomial representation and the limitations of finite approximations.

Discussion Status

The conversation is ongoing, with some participants providing suggestions such as taking the logarithm of both sides of the equation. However, there is a lack of consensus on how to achieve a polynomial form, and further clarification on the problem's requirements is sought.

Contextual Notes

There is mention of specific information needed to solve for k, but the details of this information are not provided, leading to questions about the assignment's expectations.

darthxepher
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Homework Statement



Turn y = y(0) * e^(-kt) into a polynomial.


Homework Equations





The Attempt at a Solution



I have no idea of how I would go about doing this. I know you can use taylor series to approximate it, but is there any other way?

Thanks,

Darthxepher
 
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Well, no. exp(-kt) isn't a finite degree polynomial in t. You can only approximate it with polynomials. There are other approximations besides taylor series, but I'm not really sure what you are asking.
 
The assignment is to find some value of k given some information, but the assignment wants us to convert that expression into a polynomial then solve for k. Does that make sense?
 
Take the log of both sides of the equation.
 
Ya i did that, then solved for k but that still doesn't give me a polynomial... :P
 
then perhaps you should tell us what the problem really is- what the "some information" that is given?
 

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