Exponential revision question I can't work out?

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Homework Help Overview

The discussion revolves around a problem in calculus involving the manipulation of an equation to isolate the variable "t". The original equation presented is "i=12.5(1-e^-t/cr)", and the goal is to make "t" the subject. Participants are exploring the steps necessary to transpose the equation correctly, particularly focusing on the use of natural logarithms.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to isolate the exponential term before applying logarithms. There is confusion about how to correctly manipulate the equation, particularly regarding the placement of the constant "1" and the implications of moving terms across the equation. Some participants suggest various interpretations of the equation's structure, leading to questions about the correct approach to transposition.

Discussion Status

The discussion is ongoing, with participants providing hints and guidance on how to proceed with the algebraic manipulation. There is a recognition of the need to clarify the steps involved in removing the constant from the right side of the equation. Multiple interpretations of the equation are being explored, and participants are actively questioning each other's reasoning without reaching a consensus.

Contextual Notes

Participants note that the original equation's structure may lead to different interpretations, which complicates the transposition process. There is also mention of the variables involved, such as resistance and capacitance, which may affect the context of the problem.

  • #31
opps sorry that should be -i/12.5-1=e-t/cr
 
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  • #32
Ramjam said:
opps sorry that should be -i/12.5-1=e-t/cr
No, that's not right either. You really need to be more careful.
 
  • #33
in that case i don't under what you mean by
After you multiplied by -1, what happened to the -1?
 
  • #34
What is -1 times i/12.5 - 1?

If you're having such a difficult time with basic algebra, I am very concerned about the prospects of you working with exponential and log equations.
 
  • #35
Mark44 said:
What is -1 times i/12.5 - 1?

If you're having such a difficult time with basic algebra, I am very concerned about the prospects of you working with exponential and log equations.
It was 2am in the uk and after a long working day which i also do along side my course probably wasn't the best idea.

Right here are my working so far now that I've been had some sleep,

we start with I=12.5(1-e-t/cr)

I then divide both sides by 12.5 removing the 12.5 from the right hand side.

I/12.5 = 1-e-t/cr

I then subtract -1 from both sides

I/12.5 -1 = -e-t/cr

I then times both sides by -1 giving me

(1- I/12.5) = e-t/cr

how ever to remove I am unsure of how to go on from here?
 
  • #36
You need the time when the current I reaches the value I=10 A. Note that 12.5 is also in amperes. Substitute 10 for I and evaluate the left side of the equation.
Also calculate cr, or better CR from the given value of capacitance C and resistance R.
 

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