Approximation for the Exponential

In summary, the speaker is having difficulty evaluating e^{-x} without the use of a calculator. They mention trying to use a Taylor series but finding it unwieldy. They also apologize for not being able to solve this problem without a calculator despite having a B.S. in physics. Another person suggests using a scientific calculator and practicing with it since calculators are not allowed on the GRE. The speaker also mentions the importance of knowing the value of log10e for making rough estimates.
  • #1
moonjob
11
0
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
[itex]e^{-x}[/itex].

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

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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  • #2
"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!
 
  • #3
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!
 
  • #4
If you keep in your own memory (brain not computer) log10e, it will help you get ball park estimates for ex.
 

FAQ: Approximation for the Exponential

1. What is an exponential function?

An exponential function is a mathematical function in which the input variable, also known as the independent variable, is an exponent. This means that the value of the function increases or decreases rapidly as the input variable increases.

2. What is the importance of approximation for exponential functions?

Approximation for exponential functions is important because many real-world phenomena can be modeled using exponential functions. However, these functions can be difficult to solve exactly, so approximation methods are used to find approximate solutions that are close enough for practical purposes.

3. What are some common methods for approximating exponential functions?

Some common methods for approximating exponential functions include Taylor series, Euler's method, and the Runge-Kutta method. These methods use a series of calculations to estimate the value of an exponential function at a given point.

4. How accurate are these approximation methods?

The accuracy of the approximation methods for exponential functions depends on various factors such as the complexity of the function and the number of terms used in the calculation. Generally, the more terms used, the more accurate the approximation will be. However, it is important to note that these methods will always provide an estimate and not an exact solution.

5. Can approximation for exponential functions be used in real-world applications?

Yes, approximation for exponential functions is commonly used in various fields such as finance, physics, and engineering. For example, in finance, exponential functions are used to model compound interest, and in physics, they are used to model radioactive decay. Approximation methods allow us to make predictions and solve problems related to these real-world applications.

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