双倍时间公式

双倍时间可以定义为任何以一定速度增长的数量变成初始大小/数量两倍的时间。当被要求找出任何事物的价值将翻倍的时间时，倍增时间有助于使单利或利率增长的计算变得更加容易。

双倍时间公式

In the below given double-time formula, we have taken the natural log and r is the rate of growth.

Double Time Formula = $\frac{log2}{log(1+ r)}$

If the growth rate is given in percentage then double time can be calculated by modifying the formula so the new formula is,

Double time formula = 70/r

Here r is the percentage growth rate.

This new formula is also known as the Rule of 70 because in the above formula the double-time has been calculated by dividing 70 by r which represents the percentage rate of growth. 

双倍时间配方的特点

1. 只用增长率就可以很容易地找到双倍时间。
2. 它用于不同的现实世界方面，如一个国家的人口增长、资源利用、单利和复利等。
3. 它清楚地显示了某项投资在一段时间内获得的利润。
4. 双倍时间公式是一个非常古老的概念，它在巴比伦被用来计算给定贷款的利息。

示例问题

问题1：每年10%的增长率翻一番需要多少年。

解决方案：

To find the time we will use double time formula

Double Time Formula = log2/log(1+ r)

Here r is given as 10% so r= 10/100 = 0.10

Double time = log2/log(1 + 0.10)

= 7.27 years

Hence it will take about 7.27 years to double the amount.

问题 2：使用七十法则求一个国家的当前人口在年增长率为 5% 的情况下翻倍的时间。

解决方案：

Given r = 5%

So using rule of 70

Double time = 70/r

= 70/5

= 14

Hence it will take 14 years for the population to get double.

问题 3：求增长率使给定的数量在 10 年内翻一番。

解决方案：

We need to find the r and double time is given which is 10 years.

Now using the rule of 70

Double time = 70/r

10 = 70/r

r = 70/10

r = 7 

Hence rate is 7% per annum.

问题4：每年18%的增长率翻一番需要多少年。

解决方案：

To find the time we will use double time formula

Double Time Formula = log2/log(1 + r)

Here r is given as 18% so r= 18/100 = 0.18

Double time = log2/log(1 + 0.18)

= 4.18 years

Hence it will take about 4.18 years to double the amount.

问题 5：在池塘中细菌以 7% 的速度增加，找到它翻倍的时间。

解决方案：

To find the time we will use double time formula

Double Time Formula = log2/log(1 +  r)

Here r is given as 7% so r= 7/100 = 0.07

Double time = log2/log(1 + 0.07)

= 10.24 years

Hence it will take about 10.24 years to double the bacteria in the pond.

问题 6：求增长率使给定的数量在 20 年内翻一番。

解决方案：

We need to find the r and double time is given which is 20 years.

Now using the rule of 70

Double time = 70/r

20 = 70/r

r = 70/20

r = 3.5

Hence rate is 3.5% per annum.

问题 7：使用 70 法则求当一个池塘的当前细菌数量以每年 7% 的速度增长一倍的时间。

解决方案：

Given r = 7%

So using rule of 70

Double time = 70/7

= 70/7

= 10

Hence it will take 10 years for the population to get double.