Is it Possible to solve Exponential Equations like these?

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Homework Help Overview

The discussion revolves around solving an exponential equation related to modeling exponential growth and decay. The original poster questions the possibility of finding an algebraic solution to the equation involving exponential terms.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the nature of the equation, noting that it is transcendental and may not have an algebraic solution. There are attempts to isolate exponential terms and explore numerical or graphical methods for finding solutions.

Discussion Status

Some participants have provided insights into the limitations of algebraic solutions for this type of equation and suggested numerical approaches. Others have offered specific observations about the relationship between the exponential terms, indicating a potential direction for further exploration.

Contextual Notes

Participants are considering the implications of the equation's structure and the nature of exponential functions, as well as the constraints of algebraic methods in this context.

Alex Myhill
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Homework Statement


Hi, I have come across this equation in modelling exponential growth and decay. I am wondering if it is possible to solve it algebraically or not?

Homework Equations


8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x)

The Attempt at a Solution


Brought all e^(ax) values to one side, however beyond that step I am really not sure of where to go, have looked at the problem for several hours without any results, any help would be appreciated.
 
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Alex Myhill said:

Homework Statement


Hi, I have come across this equation in modelling exponential growth and decay. I am wondering if it is possible to solve it algebraically or not?

Homework Equations


8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x)

The Attempt at a Solution


Brought all e^(ax) values to one side, however beyond that step I am really not sure of where to go, have looked at the problem for several hours without any results, any help would be appreciated.
In general, there is no algebraic method to solve such equations since they are transcendental rather than algebraic by nature.

Only a numerical or graphical solution can be obtained. Iteration using different trial values of x is probably the quickest way to find a solution here.
 
Hi SteamKing, thankyou for your answer, I have learned something from that.
 
In this particular equation, you can easily see that the second exponential expression is likely to be about half the first, so x must be about 10.
You could then rewrite the .7895x as .763x+.0265x, or approximately .763x+0.265. That should get you to a reasonably accurate answer. You could redo that with the more accurate x value as a check.
 

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