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An algorithm that completes in "polynomial time" is faster to solve than an algorithm that completes in "exponential time" in most of the important cases where it needs to be solved.

An algorithm that completes in "polynomial time" the time to solve is always determinable by a polynomial equation (e.g. x^2, x^4+7*x^3+12*x^2+x+19, x^8392).

An algorithm that completes in "exponential time" the time to solve can only be determined an exponential equation (e.g. 2^x, e^x, 10^x, 982301^x).

Exponential equations give larger value answers than polynomial equations after a certain input value and then increase progressively faster. This makes "exponential time" algorithms take much longer than "polynomial time" algorithms to solve, often making many of them effectively unsolvable for certain cases.

Many of the most important algorithms needed to solve real world problems are "exponential time" algorithms.

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