Approximation for the Exponential

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Discussion Overview

The discussion revolves around methods for approximating the value of the exponential function \( e^{-x} \), particularly in the context of preparing for the GRE exam without the use of a calculator. Participants explore various techniques and express concerns about the feasibility of manual calculations.

Discussion Character

  • Homework-related
  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant mentions considering the Taylor series for approximating \( e^{-x} \), but finds it unwieldy.
  • Another participant questions the practicality of performing calculations without a calculator, highlighting the time-consuming nature of manual computations.
  • A suggestion is made to memorize \( \log_{10} e \) to facilitate ballpark estimates for exponential calculations.
  • There is a reiteration that calculators are not permitted on the GRE, which adds to the challenge of estimating values accurately.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of calculating \( e^{-x} \) without a calculator, with some emphasizing the difficulty of manual methods while others suggest memorization techniques. There is no consensus on a specific method for approximation.

Contextual Notes

The discussion does not resolve the limitations of the proposed methods, such as the accuracy of estimates or the specific conditions under which they may be applied.

Who May Find This Useful

Students preparing for standardized tests like the GRE, particularly those interested in mathematics and physics, may find this discussion relevant.

moonjob
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I have been studying for the GRE and taking note of various approximations to use on the exam, but I am having a difficult time finding a way to evaluate the following without the aid of a calculator
e^{-x}.

The GRE practice book has a problem to which the answer is
e^{-10} = 4.5 \times 10^{-5}.

I thought of using a Taylor series, but that is unwieldy... as were some other methods that I thought of.

I apologize if this is something I should know already... being that I have a B.S. in physics, but I'm really stuck here and I don't want to miss a problem like this just because I don't have a calculator.
 
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"I don't have a calculator."

What the hey!? For starters, even "fast" algorithms implemented in compilers involve a lot of floating point operations -- you'd lose a lot of time pencil & papering (or even abacusing) trying to do those by hand. Also, what are you going to do if a problem requires trig functions?

Anyhow, you can get a decent scientific calculator for under $10: http://www.officeworld.com/Worlds-Biggest-Selection/CSOFX260SOLAR/11Q3/ , for example. Go get one and spend a couple of hours getting familiar with it -- you'll have a lot of competition on the GRE. BTW, good luck!
 
obafgkmrns said:
"I don't have a calculator."

What the hey!? For starters, even "fast" algorithms implemented in compilers involve a lot of floating point operations -- you'd lose a lot of time pencil & papering (or even abacusing) trying to do those by hand. Also, what are you going to do if a problem requires trig functions?

Anyhow, you can get a decent scientific calculator for under $10: http://www.officeworld.com/Worlds-Biggest-Selection/CSOFX260SOLAR/11Q3/ , for example. Go get one and spend a couple of hours getting familiar with it -- you'll have a lot of competition on the GRE. BTW, good luck!

Thank you for the reply, but I actually meant that I won't be able to use a calculator. It's not allowed on the GRE!
 
If you keep in your own memory (brain not computer) log10e, it will help you get ball park estimates for ex.
 

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