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And so when we say something is exponential, we're talking about in terms of the number of bits required to represent it.
所以当我们说某些东西，是指数增长的我们指的,就是代表它的比特数。
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And in fact, if you look at the top figure it looks as exponential or, quadratic isn't even growing at all.
它看上去是指数型的,而幂次型的看上去,根本没有增长。
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This is an example of an exponential growth process and you're familiar with processes like these.
这是一个指数增长的过程,你们应该都很熟悉的
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Because we underestimate the growth of exponential function.
因为我们低估了指数函数的增长。
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So I haven't done magic, I've given you a really fast way to solve a knapsack problem, but it's still exponential deep down in its heart, in something.
所以我并没有施魔法，我已经告诉了你,一种快速解决背包问题的方法了,但是某些方面它的核心仍然是指数增长的。
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And what we want to do then, is we want to basically come up with, how do we characterize the growth-- God bless you-- of this problem in terms of this Quadra-- sorry, terms of this exponential growth.
现在我们想要做的就是,我们怎么来量化增长率呢？,在这个问题中也,就是框架-对不起是，输入指数的增长。
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This is one of these properties of this kind of exponential growth.
这就是这种,指数增长问题的特性。
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I could get a really big upper bound, this thing grows exponentially.
那么我可以得出一个相当大的上界，我们可以给一个指数级增长的上限。
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You see how really fast exponential growth is?
你看到指数增长有多恐怖了吧？
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But this thing grows exponentially.
但是这种增长是指数性的。
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One of the interesting properties of cells that are in exponential growth is that the time to increase the cell number by a factor of 2 is always the same.
细胞有一个有趣的性质,那就是在指数增长阶段,细胞增长的速度,永远是以二为底数来增长的
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But effectively it is, as we saw before, exponential.
但是实际上正如我们之前看到的，它是指数增长的。
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But it's not 2 to the something.
它差不多是指数增长的。
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