Analysis: If the monthly growth rate is X, the number of computers produced in February is 1, 200 (1+X), and in March it is 1, 200 (1+X). According to the meaning of the question, the equivalence relation is found: the number of computers produced in March is 2700, and the equivalence relation is found accordingly.
Solution: solution: let the monthly growth rate be x, according to the meaning of the question:
The equation is 1200 (1+x) 2 = 2700.
2. The number of senior high school students in a certain district was 5,000 in 2004 and 7,200 in 2006. If the number of people taking the senior high school entrance examination is the same every year, then this is.
Analysis: The problem is the average annual growth rate from 2004 to 2006. In 2004, 5000 students took the senior high school entrance examination, and in 2006, 7200 students took the senior high school entrance examination. Let the growth rate be x, and according to the number of people after growth = the number before growth (1+ growth rate), that is, the number of people in 2005 is 5000 (1+x), and the number of people in 2006 is 5000 (1+x)2, the equations can be solved accordingly.
A: A: The average annual growth rate is X, which means yes.
5000( 1+x)2=7200
Solution: (1+x)2=, 1+x =
X 1=20%, x2=-2.2 (omitted)
A: In the past two years, the number of people taking the senior high school entrance examination has increased by 20%.
3. 165438+ 10, the output of a coal plant in October is 60000t, and the output in February is 65438+66000t. Let x be the equation, which can be listed as.
Solution: The countable equation is: 6×( 1+x)=6.6.
The solution is x = 10%.
The output value of a factory in January is 500,000 yuan. If the total output value in the first quarter is 320,000 yuan more than that in January, find the monthly average. If the monthly average is x, the following equation can be obtained
Analysis: This question is about the growth rate. Quantity after general growth = quantity before growth ×( 1+ growth rate). If the average monthly growth rate is x, then the monthly output of this quarter is 50,50( 1+x) and 50( 1+x)2 respectively, and then according to the meaning of the question,
Solution: Solution: If the average monthly growth rate is x,
Then the monthly output of this quarter is 50,50( 1+x), 50( 1+x)2,
∴50+50( 1+x)+50( 1+x)2= 150+32.
So the answer to the fill-in-the-blank question: 50+50 (1+x)+50 (1+x) 2 =150+32.
5. A factory produces 500 tons of chemical fertilizer in January and 720 tons in March, so what is the average month of the factory in the first quarter? Solution: Let the month be X, which is derived from the meaning of the question, and the equation is listed as:
Solution: let the average monthly growth rate of the factory in the first quarter be x,
List the equation according to the meaning of the question: 500 (1+x) 2 = 720.
6.(2000? Shaanxi) an economic development zone, the industrial output value reached 5 billion yuan this year 1 month, and the total output value in the first quarter was 654.38+075 billion yuan. What is the monthly average in February and March? If the monthly average is x, according to the meaning of the question, the equation can be listed as ().
a、50( 1+x)2= 175 B、50+50( 1+x)+50( 1+x)2 = 175 C、50( 1+x)+50( 1+x)2 = 175
d、50+50( 1+x)2= 175
Solution: Solution: February output value 50( 1+x).
The output value in March is: 50 (1+x) (1+x) = 50 (1+x) 2,
Therefore, the total output value in the first quarter is: 50+50 (1+x)+50 (1+x) 2 =175.
So choose B.
7. The output value of a factory in July was 6,543,800 yuan, and it is planned to reach 6,543,800 yuan in September, which is the same every month. Let this be x, and the equation can be listed according to the meaning of the question.
Solution: let this growth rate be x,
According to the meaning of the question:100 (1+x) 2 =144.
8. The turnover of a store in the fourth quarter was 364,000 yuan, and the known monthly turnover was 1 10,000 yuan. Calculate the average month of the next two months.
Analysis: The average monthly growth rate of the last two months can be set as X, and the equivalent relationship is: original quantity ×( 1+ growth rate) n= existing quantity, and n represents the number of growth times.
Answer: solution: suppose the average monthly growth rate in the last two months is x, according to the meaning of the question, you can get
10+ 10( 1+x)+ 10( 1+x)2 = 36.4，
The solution is x 1=0.2, x2=-3.2 (truncation).
A: The average monthly growth rate in the last two months is 20%.
9.(2000? A factory in Lanzhou) steel output in the first quarter 190 tons, February and March 150 tons. Find the average month.
Analysis: Suppose the average monthly growth rate is X, 1 monthly output is 190- 150=40, February output is 40( 1+x), and March output is 40( 1+x)2. According to February and March, the output is 65438.
A: A: Let the average monthly growth rate be X, depending on the meaning of the question.
The output in January is 190- 150=40, then
40( 1+x)+40( 1+x)2 = 150，
The solution is x 1=0.5=50%, x2=-3.5 (omitted).
So the average monthly growth rate is 50%.
10. A city plans to quadruple the gross industrial and agricultural production in two years, so the average annual gross industrial and agricultural production is
Analysis: This question is about the growth rate. Generally speaking, the amount after growth = the amount before growth ×( 1+ growth rate). If the average annual growth rate of industrial and agricultural GDP is x, then according to the meaning of the question, the equation can be obtained as: (1+x)2=22, and the equation can be solved.
Solution: Let the average annual growth rate of industrial and agricultural GDP be x, and get (1+x)2=22 according to the meaning of the question.
The solution is x= 1 or x=-3 (truncation).
Therefore, the average annual growth rate of industrial and agricultural GDP is 100%.