5.11 连接:随着时间推移建模大楼梯

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• Select section 连接: 建模随着时间推移建造大楼梯

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  连接: 建模随着时间推移建造大楼梯

  

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  The Grand Staircase, named by the geologist Clarence Dutton in the 1870s, is a sequence of sedimentary rock layers that go down in steps from Bryce Canyon National Park in Utah to the north rim of the Grand Canyon in Arizona ¹ . Part of the staircase was designated as Grand Staircase-Escalante National Monument by President Bill Clinton in 1996 ² . It is the largest national monument in the country. Some other sections of the staircase are part of other national monuments or national parks. 
  ::1870年代由地质学家Clarence Dutton命名的大楼梯是一系列沉积岩层,从犹他州的Bryce Canyon国家公园到亚利桑那州的Grand Canyon国家公园的北边。 1996年,比尔·克林顿总统将部分楼梯指定为Grand Staircase-Escalante国家纪念碑,这是该国最大的国家纪念碑,其他几处楼梯是其他国家纪念碑或国家公园的一部分。

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  According to Dutton, the staircase could be described with five steps—the Pink Cliffs, the Grey Cliffs, the White Cliffs, the Vermilion Cliffs, and the Chocolate Cliffs—that you can see in the image below. (Since Dutton's description, geologists have furthered divided up the layers into different rock types) ¹ . 
  ::根据Dutton的说法,楼梯可以用五个步骤来描述,五个步骤,即粉色裂缝、灰色裂缝、白色裂缝、Vermilion裂缝和巧克力裂缝,你可以在下面的图像中看到。 (由于Dutton的描述,地质学家们把层层进一步分为不同的岩石类型) 1。

  

  Grand Canyon (A), Chocolate Cliffs (B), Vermilion Cliffs (C), White Cliffs (D), Zion Canyon (E), Gray Cliffs (F), Pink Cliffs (G), Bryce Canyon (H)
  

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  We can express the formation of the layers as a function according to when the layers were formed. Let $\begin{array}{r}L\end{array}$  be the layer formed and  $\begin{array}{r}t\end{array}$  be the number of years ago (in millions) that layer was formed. 
  ::我们可以按照层形成时的功能来表达层层的形成,让L成为层,不要像几年前(以百万计)那样形成。

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  $$\begin{array}{r}L(t)=\{\begin{array}{lll}\text{Pink Cliffs}& & 50\le t\le 60\\ \text{Grey Cliffs}& & 125\le t\le 135\\ \text{White Cliffs}& & 145\le t\le 155\\ \text{Vermilion Cliffs}& & 165\le t<200\\ \text{Chocolate Cliffs}& & 200\le t\le 225\end{array}\end{array}$$

  
  ::L(t) Pink Cliffs50t60Grey Cliffs125t135 White Cliffs145t155Vermilion Cliffs165t < 200Chocoltate Cliffs200t225

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  1. Why is this a function? Explain.
  ::1. 为什么这是一项职能?

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  2. What is the domain of this function?
  ::2. 这一职能的哪些领域?

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  3. What is the range of this function?
  ::3. 这一职能的范围是什么?

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  4. What cliffs formed 175,000,000 years ago?
  ::4. 175 000 000年前,哪些悬崖形成?

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  5. What cliffs formed 150,000,000 years ago?
  ::5. 150万年前,哪些悬崖形成了150万年前的悬崖?

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  6. What cliffs formed 225,000,000 years ago?  
  
  ::6. 哪些悬崖在225 000万年前形成?

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  7. Research what types of sediment layers are in your area. Express the development of the layers as a piecewise-defined function. 
  ::7. 研究贵国区域内的沉积层类型,将沉积层的开发表现为一种按片段定义的功能。

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  by Fabio Bezoari shows some parts of the national monument.
  ::Fabio Bezoari展示了国家纪念碑的某些部分。

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  References
  ::参考参考资料

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  1. "Grand Staircase," last edited May 1, 2017,
  ::1. 2017年5月1日编辑的《大楼梯》

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  2. "Grand Staircase-Escalante National Monument," May 8, 2017, https://en.wikipedia.org/wiki/Grand_Staircase-Escalante_National_Monument.
  ::2. “Grand Staircase-Escalante National Camage”,2017年5月8日,https://en.wikipedia.org/wiki/Grand_Staircase-Escalante_National_Monument。