Approximation for the Exponential

[moonjob]

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.

 

[obafgkmrns]

"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!

 

[moonjob]

"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!

 

[mathman]

If you keep in your own memory (brain not computer) log₁₀e, it will help you get ball park estimates for e^x.