Stuck Trying to Re-arrange Variables

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Homework Help Overview

The discussion revolves around the challenge of rearranging variables in a mathematical equation, specifically focusing on solving for the variable "t" when given a value for "k." The subject area appears to involve algebra and numerical methods.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants express uncertainty about finding an algebraic solution for the equation. Some suggest numerical methods as a potential approach, while others question the feasibility of solving for "t" without additional information.

Discussion Status

The discussion is ongoing, with some participants exploring numerical methods as a viable option for finding "t." There is no explicit consensus on the best approach, but guidance towards numerical solutions has been offered.

Contextual Notes

Participants mention constraints such as often being given the value of "k" without knowing the corresponding time "t," which complicates the problem-solving process.

cgw_niu
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Homework Statement
I need to re-arrange the below statement in terms of "t"
Relevant Equations
Original Equation:

k = 1/[e^(-A*t) - e^(-B*t)]

Where k is a real number and A and B are real numbers > 1
this is as far as I get:
246511
 
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Here is the original form of the equation

246512
 
I doubt you will find any algebraic solution to that equation.
 
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HallsofIvy said:
I doubt you will find any algebraic solution to that equation.
bummer, I am often given the value of "k" but do not know at what time it happens. The only was so far is to plug and play or plot it and get a close estimate for "t". I am by far means no mathematician, but I would think there has to be a way to solve for "t" for a known value of "k". Maybe not though.
 
It's easy to solve for t numerically given the other values. A method like Newton's method should converge to a solution rapidly. That's probably what you really want.
 
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