6.16%的变化

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  In 2007, there were an estimated 80 million active users on Facebook. Between 2007 and 2015, Facebook’s active member base increased by 1,070%. That number continued to grow over time. As of March 2015, Facebook boasted 936 million active users. Approximately how many active users did Facebook have in 2015?
  ::2007年,Facebook上估计有8000万活跃用户。 2007至2015年间,Facebook的活跃成员基础增长了1070 % 。 这一数字在一段时间内继续增长。 截至2015年3月,Facebook拥有9.36亿活跃用户。 2015年Facebook拥有大约多少活跃用户?

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  In this concept, you will learn to use the percent of change to find a new  amount .
  ::在这个概念中,你将学会使用变化的百分率来寻找新的数额。

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  Using Percent of Change
  ::使用变化百分比

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  If you are given the   or the   and the original amount, you can find the new amount by using the following formula:
  ::如果给定了原始数额或原始数额,则使用以下公式可以找到新数额:

  $$\begin{array}{r}\text{Amount of change}=\text{percent of change}\times \text{original amount}\end{array}$$

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  Let’s apply this formula to a problem.
  ::让我们把这个公式应用到问题上。

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  Find the new number when 75 is decreased by 40%.
  ::当 75 减少 40% 时, 查找新数字 。

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}\begin{array}{rcl}\text{Amount of change}& =& \text{percent of change}\times \text{original amount}\\ & =& 40\mathrm{\%}\times 75\end{array}\end{array}$$

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  Next, change the percent to a decimal and multiply to find the percent of change.
  ::接下来,将百分比修改为小数点后,乘以找到变化的百分比。

  $$\begin{array}{r}\begin{array}{rcl}& =& 0.40\times 75\\ & =& 30\end{array}\end{array}$$

  
  Now, since the original number is being decreased, subtract the amount of change from the original number to find the new number.

  $$\begin{array}{r}75-30=45\end{array}$$

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  The answer is when 75 is decreased by 40%, the new number is 45.
  ::答案是当75人减少40%时, 新的数字是45人。

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  Let’s look at another example.
  ::让我们再看看另一个例子。

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  Find the new number when 28 is increased by 125%.
  ::当 28 增加 125% 时, 查找新数字 。

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}\begin{array}{rcl}\text{Amount of change}& =& \text{percent of change}\times \text{original amount}\\ & =& 125\mathrm{\%}\times 28\end{array}\end{array}$$

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  Next, change the percent to a decimal and multiply to find the percent of change.
  ::接下来,将百分比修改为小数点后,乘以找到变化的百分比。

  $$\begin{array}{r}\begin{array}{rcl}& =& 1.25\times 28\\ & =& 35\end{array}\end{array}$$

  Now, since the original number is being increased, add the amount of change to the original number to find the new number.

  $$\begin{array}{r}28+35=63\end{array}$$

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  The answer is when 28 is increased by 125%, the new number is 63.
  ::答案是当28人增加125%时, 新的数字是63人。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Facebook and its number of active users.
  ::更早之前, 脸书及其活跃用户数量出现问题,

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  The member base increased 1,070% between 2007, when it was 80 million active users, and 2015. How many active users did Facebook have in 2015?
  ::2007年是8 000万活跃用户,2015年是2015年。 2015年Facebook有多少活跃用户?

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}\begin{array}{rcl}\text{Amount of change}& =& \text{percent of change}\times \text{original amount}\\ & =& 1,070\mathrm{\%}\times 80\text{ million}\end{array}\end{array}$$

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  Next, change the percent to a decimal and multiply to find the percent of change.
  ::接下来,将百分比修改为小数点后,乘以找到变化的百分比。

  $$\begin{array}{r}\begin{array}{rcl}& =& 10.70\times 80\text{ million}\\ & =& 856\text{ million}\end{array}\end{array}$$

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  Now, since the original number is being increased, add the amount of change to the original number to find the new number.
  ::现在,既然最初的号码正在增加, 请在原来的号码上加上更改的金额, 以找到新的号码 。

  $$\begin{array}{r}80\text{million}+856\text{million}=936\text{million}\end{array}$$

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  The answer is the number of active Facebook users in 2015 was 936 million.
  ::答案是2015年Facebook活跃用户人数为9.36亿。

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  Example 2
  ::例2

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  The population of Westville grew from 25,000 to 27,000 in two years. What was the percent of increase for this period of time?
  ::Westville的人口在两年内从25 000人增长到27 000人。 这一时期的增长百分比是多少?

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  First, find the amount of the change by subtracting.
  ::首先,通过减去找到变化的金额。

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  The amount of change is  $\begin{array}{r}27,000-25,000=2,000\end{array}$
  ::变动额为27,000 -25,000=2,000

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  Next, find the percent of the increase.
  ::接下来,找到增长的百分之一。

  $$\begin{array}{r}\begin{array}{rcl}\text{Percent of increase or decrease}& =& \frac{\text{Amount of change}}{\text{Original amount}}\\ & =& \frac{2,000}{25,000}=\frac{2}{25}\\ & =& 0.08=8\mathrm{\%}\end{array}\end{array}$$

  
  

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  The answer is the population increased 8% over this period of time.
  ::答案是,在这一时期,人口增加了8%。

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  Example 3
  ::例3

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  Find the new number when 45 is increased by 10%.
  ::当 45 增加 10% 时, 查找新数字 。

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}\begin{array}{rcl}\text{Amount of change}& =& \text{percent of change}\times \text{original amount}\\ & =& 10\mathrm{\%}\times 45\end{array}\end{array}$$

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  Next, change the percent to a decimal and multiply to find the percent of change.
  ::接下来,将百分比修改为小数点后,乘以找到变化的百分比。

  $$\begin{array}{r}\begin{array}{rcl}& =& 0.10\times 45\\ & =& 4.5\end{array}\end{array}$$

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  Now, since the original number is being increased, add the amount of change to the original number to find the new number.
  ::现在,既然最初的号码正在增加, 请在原来的号码上加上更改的金额, 以找到新的号码 。

  $$\begin{array}{r}45+4.5=49.5\end{array}$$

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  The answer is when 45 is increased by 10%, the new number is 49.5.
  ::答案是 当45人增加10%时 新的数字是49.5

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  Example 4
  ::例4

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  Find the new number when 80 is decreased by 15%.
  ::当 80 减少 15% 时, 查找新数字 。

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}\begin{array}{rcl}\text{Amount of change}& =& \text{percent of change}\times \text{original amount}\\ & =& 15\mathrm{\%}\times 80\end{array}\end{array}$$

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  Next, change the percent to a decimal and multiply to find the percent of change.
  ::接下来,将百分比修改为小数点后,乘以找到变化的百分比。

  $$\begin{array}{r}\begin{array}{rcl}& =& 0.15\times 80\\ & =& 12\end{array}\end{array}$$

  Now, since the original number is being decreased, subtract the amount of change from the original number to find the new number.

  $$\begin{array}{r}80-12=68\end{array}$$

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  The answer is when 80 is decreased by 15%, the new number is 68.
  ::答案是,当80人减少15%时,新的数字是68人。

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  Example 5
  ::例5

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  Find the new number when 50 is increased by 25%.
  ::在50增加25%时找到新数字。

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  First, find the amount of change.
  ::首先,找到变化的金额。

  $$\begin{array}{r}\begin{array}{rcl}\text{Amount of change}& =& \text{percent of change}\times \text{original amount}\\ & =& 25\mathrm{\%}\times 50\end{array}\end{array}$$

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  Next, change the percent to a decimal and multiply to find the percent of change.
  ::接下来,将百分比修改为小数点后,乘以找到变化的百分比。

  $$\begin{array}{r}\begin{array}{rcl}& =& 0.25\times 50\\ & =& 12.5\end{array}\end{array}$$

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  Now, since the original number is being increased, add the amount of change to the original number to find the new number.
  ::现在,既然最初的号码正在增加, 请在原来的号码上加上更改的金额, 以找到新的号码 。

  $$\begin{array}{r}50+12.5=62.5\end{array}$$

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  The answer is when 50 is increased by 25%, the new number is 62.5.
  ::答案是,当50人增加25%时, 新的数字是62.5。

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  Review
  ::回顾

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  Find the percent of change and then use it to find a new amount.
  ::找到变化的百分比,然后用它来寻找新的数额。

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  1. 25 decreased by 10%
     ::25 减少10%
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  2. 30 decreased by 15%
     ::30 减少15%
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  3. 18 decreased by 10%
     ::18 减少了10%
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  4. 30 decreased by 9%
     ::30人减少9%
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  5. 12 decreased by 12%
     ::12 减少12%
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  6. 90 decreased by 14%
     ::90人减少了14%
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  7. 200 decreased by 80%
     ::200人减少80%
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  8. 97 decreased by 11%
     ::97年减少了11%
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  9. 56 decreased by 25%
     ::56人减少25%,减少25%
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  10. 15 decreased by 20%
      ::15人减少20%
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  11. 220 decreased by 5%
      ::220人减少了5%
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  12. 75 decreased by 10%
      ::75人减少10%
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  13. 180 decreased by 18%
      ::180减少18%
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  14. 1500 decreased by 12%
      ::1500下降了12%
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  15. 18,000 decreased by 24%
      ::减少了18,000人,减少了24%

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  Review (Answers)
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源