, n is the interval period and r is the average growth rate.
When the passage period is the same, that is, n is the same, and the topic makes the comparative average growth rate r larger, we can convert the formula into just comparison.
Let's practice through examples.
Example 1(20 17- national examination-130) can be deduced from the above data:
From 2000 to 20 15, among the five technical patents, the annual growth rate of parts manufacturing was the fastest.
B From 20 1 1 to 20 15, the number of patent applications for energy storage device manufacturing is more than three times that for motor manufacturing.
In c 20 10, the number of patent applications for manufacturing energy supply devices quadrupled compared with 2005.
D 200 1-20 15 years, the year in which the number of patent applications for manufacturing energy storage devices increased the most was 20 10 years.
analyse
Item a: by? The fastest annual growth rate? Judge and examine the comparison of the average annual growth rate, because they are all? 2000-20 15? By comparing the size, it is not difficult to find that during 2000-20 15, only the number of patent applications for spare parts manufacturing was 0, and all other items were less than 10, so its annual growth rate was the fastest, and A was correct;
When the topic requires calculating the specific value of the average growth rate, it is easy to find that it needs to be calculated to the n power of 1+r 0+R, and there is no calculator in the examination room, so the calculation is too complicated. Here, I will introduce the interpolation method to you.
Example 2 The following description is correct:
A. The annual growth rate of mobile broadband users is faster than that of fixed Internet broadband access users for four consecutive years.
In b 20 17, the total number of mobile broadband users and fixed internet broadband access users increased by about 2.5 times compared with 20 13.
C from 20 13 to 20 17, the average annual growth rate of fixed internet broadband access users is about 16.8%.
D From 20 13 to 20 17, the year with the slowest annual growth rate of fixed Internet broadband access users is 20 15.
analyse
C option, according to the formula of annual average growth rate
, can be substituted to see if the equation is established, but it requires a lot of calculation, so you can consider using interpolation:
All data are estimated with two digits reserved. According to the chart, the number of broadband access users in 20 1889 1 fixed Internet is estimated to be 19, and about 35 users in 20 17 years. At this time, the fixed Internet broadband access users are 14, 15 and 65438+. In this problem, 20 14 can be coded as 25, 20 15 can be coded as 28, and 20 16 can be coded as 30, and the interval between 2013 and 2017 is four years, so the annual growth rate is calculated and divided by 4.
The year from 13 to 14 is:? 32%
14~ 15: = 12%
The year from 15 to 16 is:? 7%
16 to 17 in recent years:? 16.7%
(32%+ 12%+7%+ 16.7%)? 4? 16.9% is very close to 16.8%, and the c option is correct.