Lesson plan
Double exponential function
A double exponential function is a constant raised to the power of an exponential function. The general formula is f(x) = a^{b^x}=a^{(b^x)} (where and ), which grows much more quickly than an exponential function. For example, if : * * * * * * . Factorials grow faster than exponential functions, but much more slowly than double exponential functions. However, tetration and the Ackermann function grow faster. See Big O notation for a comparison of the rate of growth of various functions. The inverse of the double exponential function is the double logarithm . The complex double exponential function is entire, because it is the composition of two entire functions f(x)=a^x=e^{x\ln a} and g(x)=b^x=e^{x\ln b} .
Article summary
A double exponential function is a constant raised to the power of an exponential function. The general formula is f(x) = a^{b^x}=a^{(b^x)} (where and ), which grows much more quickly than an exponential function. For example, if : * * * * * * . Factorials grow faster than exponential functions, but much more slowly than double exponential functions. However, tetration and the Ackermann function grow faster. See Big O notation for a comparison of the rate of growth of various functions. The inverse of the double exponential function is the double logarithm . The complex double exponential function is entire, because it is the composition of two entire functions f(x)=a^x=e^{x\ln a} and g(x)=b^x=e^{x\ln b} .
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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