"Practical Problems and Quadratic Equations of One Variable" PPT Courseware 2 of Quadratic Equations of One Variable

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"Practical Problems and Quadratic Equations of One Variable" PPT Courseware 2 of Quadratic Equations of One Variable

Two years ago, the cost of producing 1 ton of Class A drugs was 5,000 yuan, and the cost of producing 1 ton of Class B drugs was 6,000 yuan. With the advancement of production technology,

The current cost of producing 1 ton of Class A drugs is 3,000 yuan, and the cost of producing 1 ton of Class B drugs is 3,600 yuan. Which drug has a greater annual average cost reduction rate?

Analysis: The average annual decrease in the cost of Class A drugs is

(5000-3000)÷2=1000(yuan)

The average annual decrease in the cost of Class B drugs is

(6000-3600)÷2=1200(yuan)

The average annual decrease in the cost of Class B drugs is larger. However, the average annual decrease (yuan) is not equivalent to the average annual decrease rate (percentage)

summary

Similarly, this problem of growth rate is common in real life and has a certain pattern.

If the average growth (or decrease) percentage is b.

practise:

1. The total output of a factory in January this year was 500 tons, and the total output in March was 720 tons. The average monthly growth rate is x, and the equation is ( )

A.500(1+2x)=720 B.500(1+x)2=720 C.500(1+x2)=720 D.720(1+x)2=500

2. A school’s investment in experimental equipment last year was 20,000 yuan, and the total investment this year and next is expected to be 80,000 yuan. If the average growth rate of the school’s investment in experimental equipment this year and next is x, then the equation can be formulated for .

3. Beautifying the city and improving people's living environment has become an important part of urban construction. In recent years, a certain city has continued to increase the area of ​​urban green space through measures such as demolishing old houses, planting grass, planting trees, and building parks (as shown in the figure).

(1) Answer the following questions based on the information provided in the figure: The green space area at the end of 2001 was ________ hectares, an increase of ________ hectares from the end of 2000; in the three years of 1999, 2000, and 2001, the green space area The largest area increase occurred in __________ year;

(2) In order to meet the needs of urban development, it is planned to increase the urban green space area to 72.6 hectares by the end of 2003. Find the average annual growth rate of green space area in 2002 and 2003.

Solution: Suppose the average annual growth rate of green space in 2002 and 2003 is x. According to the meaning of the question, we get

60 (1+x)2＝72.6．

(1+x)2=1.21．

∴1＋x=±1.1.

∴ x1 = 0.1=10%,

x2 =-2.1 (does not meet the meaning of the question, discard it)

Answer: The average annual growth rate of green space area in 2002 and 2003 was 10%.

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Update Time: 2024-09-04

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