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So now I've got this gamma placed in there, -1 gamma minus 1, so I've ben feeling a little bit better.
这样我把这里的指数，换成γ,这样看起来舒服一些。
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You know, Baidu was founded at the beginning of 2000, and quickly NASDAQ reached its historical high of 5,000.
百度成立于2000年初，不久，纳斯达克指数创下5000点的新高。
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Don't be intimidated. Even though it is apparently exponential, a lot of times you can actually solve it much, much faster.
别怕，即使它,很明显是指数型的，很多时候,你都能更快的解决它。
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If one follows a diet that would be derived from the glycemic index; you're likely to have a pretty healthy diet.
如果一个人遵循基于血糖指数的饮食计划,你会得到一个相当健康的饮食
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I managed to find price indexes for Norway and Netherlands going back to 1890 and compared that with the U.S.
我找到了挪威和荷兰1890年的,价格指数数据,和当时的美国作比较
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% Alright. The Fed fund's rate is now at 3 percent, 12,500 the Dow Jones Industrial Average at about 12,500.
好吧，目前美联储的基金利率为，而道琼斯工业平均指数大约在。
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So let's understand: what is the nature of exponential function so that we can understand the power of one?
让我们先理解指数函数的本质,以便理解“一“的力量？
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You see the difference in electronegativity, square it, multiply it by one-quarter and raise that to the power e.
你看到了电负性的差异，开方，乘以四分之一,在移到e上去做指数。
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We take this Cv and put in the exponent here R right. And we put this R up in the exponent here.
我们把这个Cv提出来,放在这里的指数上，好吧？然后把。
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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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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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So if you think about the way something like, say, Mapquest works, and last week in recitation you looked at the fact that shortest path is exponential.
所以如果你想想电子地图，还有上周学的列举法,你就会发现一般最简单的方法,都是指数递增的。
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Now we talked before about a diet that would follow the glycemic index, that's another pretty helpful method to follow.
我们之前还谈论过,基于血糖指数的饮食法,那是另一种健康饮食法之一
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And it's just gathering together the multiplications while counting down the exponent. And you can see it when we get down to the end test here, we're going to pop out of there and we're going to return the answer.
这个方法就是通过乘法,来一个一个的减小指数,可以看到,最后面的结果测试，我们会在这里退出,然后返回答案。
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And if you look at this series, the series log of one, what is the series expansion?
如果你们看这个式子，它的对数分之一，它的指数是多少？
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Or just have the good intentions without the effort that's necessary to bring about a positive exponential function.
还是只有好的意图但不付出,必要的努力发挥正面指数函数的作用。
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The one that just came out is the Consumer Confidence Index which was a Conference Board publication.
浮现出来的指示器是,消费者价格指数,是世界大型企业联合会公布的。
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Like you wouldn't expect bananas, for example, to be a high glycemic index food but it is.
比如,你可能不认为香蕉,是一种高血糖指数的食物,但它确实是
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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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OK. And then the exponentials, as you saw is when typically I reduce the problem of one size into two or more sub-problems of a smaller size.
好，然后说到指数级，正如你所见，典型的例子是,我讲一个问题分解成为,两个更小规模的子问题。
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There's a tendency for people to say, oh this problem's exponential, I can't solve it.
人们往往会说，哦这是个指数型的问题我没法解决它。
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These are the only countries that I've been able to find that have high-quality, repeat sales price indexes going back a hundred years.
只有这三个国家,在100年前就已经出现,优质的重复销售价格指数
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Well, I solve 2 or 3 exponential problems before breakfast every day. You know things like, how to find my way to the bathroom is inherently exponential, but I manage to solve it anyway.
你要知道如何找到,我的浴室就是一个，固有的指数型问题,但是我还是能解决它。
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Because in "Pay it Forward", they capture this very idea of human networks as exponential functions.
电影“让爱传出去，深刻地描述了,人类网络是指数函数的观点。
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And finally, we saw an example of an exponential algorithm, those Towers of Hanoi.
最后，我们来看一个,指数算法的例子，汉诺依塔的例子。
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So, as I said, there are many graphs around many charts of the high and low glycemic index foods and some things would surprise you.
如我所说,会有许多高血糖指数的食物,和低血糖指数的食物的图表,有些东西会让你惊讶
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Again, misleading-- fail to understand it because we don't understand the nature of exponential change.
再一次，误导…,没有理解指数函数，因为我们不理解,指数变化的本质。
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Here's ten years worth of data from the Frank Russell Corporation, the benchmark Wilshire 5000.
这是来自罗素公司的,十年数据,道琼斯威尔希尔5000指数
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In some foods, those with a high glycemic index create a spike in blood sugar.
在一些食物中,一些血糖指数高的食物,会形成一个血糖峰值
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On Thursday we'll do a more careful analysis and try and understand how I could have accomplished this seemingly magical task of solving an exponential problem so really quickly.
在周四的时候,我们会做进一步的分析,并且尝试理解我为什么,能如此快速的解决这种,看上去超复杂的指数型问题。
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