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关于增长率的有关知识,在小学里我们就学过.例如.某钢铁厂第一年的产量是100万吨,第二年的产量是120万吨,第二年比第一年增加的百分数.(120-100)/100=0.2=20%即为增长率.如果每年比上一年增加的百分数相同,就称它为年平均增长率.那么上例中,如果年平均增长率为20%,第三年(即经过两年)的产量是100(1+20%)(1+20%)=100(1+20%)~2=144(万吨).一般来说,设原来的年产量为 a,年平均增长率为 x,那么经过一年的年产量等于 a(1+x),经过两年的年产量等于 a(1+x)~2,经过三年的年产量等于 a(1+x)~3,经过 n 年的年产量等于 a(1+x)~n.对于增长率的问题,都可应用上述关系式.例1 苏州服装厂1989年生产某种服装100万件,由于加快了改革开放的步伐,1991年生产这种服装625万件,求这两年平均每年增长的百分率.(1992年苏州市中考试题)
With regard to the knowledge of the growth rate, we learned in elementary schools. For example, the output of a steel mill in the first year was 1 million tons, and the output in the second year was 1.2 million tons, and the second year was a percentage increase from the first year. (120-100)/100=0.2=20% is the growth rate. If the annual percentage increase from the previous year is the same, it is called the average annual growth rate. In the above example, if the average annual growth rate is 20% In the third year (ie after two years) the output is 100 (1+20%) (1+20%)=100 (1+20%)~2=144 (ten thousand tons). In general, the original The annual output is a, the average annual growth rate is x, then the annual output after one year is equal to a(1+x), after two years the annual output is equal to a(1+x)~2, and the annual output after three years is equal to a(1+x)~3, the annual output after n years is equal to a(1+x)~n. For the problem of the growth rate, the above relation can be applied. Example 1 Suzhou Garment Factory produces certain garments in 1989 100 Ten million, due to the acceleration of the pace of reform and opening up, production of 6.25 million pieces of clothing in 1991, seeking the percentage of annual growth in the average of the two years. (Suzhou City Examination Questions in 1992)