函数模型及其应用VIP

1、函数模型及其应用 1.如何构建合适的函数模型？ 1.下表是某种车的车速与刹车后的停车距离。车速车速km/h101530405060708090100停车距离m471218253443546680（1）根据上表数据，建立车速和刹车后停车距离间的函数关系。7374. 21256. 00064. 02xxy 思考、讨论： 请根据你得到的模型，试解释为什么中华人民共和国道路交通安全法规定：机动车在高速公路上行驶，车速超过每小时100公里时，安全车距为100米以上；车速低于每小时100公里时，最小安全车距不得少于50米？你对高速公路管理部门有什么新的建议？ 2Some Chemistry student

2、s measured the concentration of chlorine remaining in a swimming pool over a period of 8 hours on a hot summer day. Chlorine had been placed in the pool at 8 am. Their results were as follows.MorningAfternoonTime91011121234Chlorine concentration(ppm)5.03.82.92.21.61.20.90.7a. Use the calculator to f

3、ind the relationship between the chlorine concentration and the time elapsed since the chlorine was placed in the pool.b. Whats the concentration of chlorine had been placed at 8 am ?tey28. 072. 60tppmy72. 6LetThe concentration of chlorine had been placed is 6.72ppm小结：1.如何构建合适的函数模型？步骤：1.画散点图2.利用判断模型

4、的适用性 越接近于1，模型越合适。3.写出函数解析式2R2R2. 函数模型的应用ExampleSome Chemistry students measured the concentration of chlorine remaining in a swimming pool over a period of 8 hours on a hot summer day. Chlorine had been placed in the pool at 8 am. Their results were as follows.MorningAfternoonTime91011121234Chlorine

5、 concentration(ppm)5.03.82.92.21.61.20.90.71.Use the calculator to find the relationship between the chlorine concentration and the time elapsed since the chlorine was placed in the pool.2.Use the results to find the concentration that would be needed at 8 am on a similar day to ensure that the chlo

6、rine concentration did not fall below 1.5ppm (parts per million) before 3 pm.3.If two chlorine doses were used , one at 8 am and another at 12 noon, what concentrations would be needed at these times to ensure that the concentration did not fall below 1.5 ppm before 3 pm.4.What are the implication o

7、f your answers for the effective chlorination of pools at lowest cost?ExampleSome Chemistry students measured the concentration of chlorine remaining in a swimming pool over a period of 8 hours on a hot summer day. Chlorine had been placed in the pool at 8 am. Their results were as follows.MorningAf

8、ternoonTime91011121234Chlorine concentration(ppm)5.03.82.92.21.61.20.90.71.Use the calculator to find the relationship between the chlorine concentration and the time elapsed since the chlorine was placed in the pool.2.Use the results to find the concentration that would be needed at 8 am on a simil

9、ar day to ensure that the chlorine concentration did not fall below 1.5ppm (parts per million) before 3 pm.3.If two chlorine doses were used , one at 8 am and another at 12 noon, what concentrations would be needed at these times to ensure that the concentration did not fall below 1.5 ppm before 3 p

10、m.4.What are the implication of your answers for the effective chlorination of pools at lowest cost?ExampleSome Chemistry students measured the concentration of chlorine remaining in a swimming pool over a period of 8 hours on a hot summer day. Chlorine had been placed in the pool at 8 am. Their res

11、ults were as follows.MorningAfternoonTime91011121234Chlorine concentration(ppm)5.03.82.92.21.61.20.90.71.Use the calculator to find the relationship between the chlorine concentration and the time elapsed since the chlorine was placed in the pool.2.Use the results to find the concentration that woul

12、d be needed at 8 am on a similar day to ensure that the chlorine concentration did not fall below 1.5ppm (parts per million) before 3 pm.3.If two chlorine doses were used , one at 8 am and another at 12 noon, what concentrations would be needed at these times to ensure that the concentration did not

13、 fall below 1.5 ppm before 3 pm.4.What are the implication of your answers for the effective chlorination of pools at lowest cost?ExampleSome Chemistry students measured the concentration of chlorine remaining in a swimming pool over a period of 8 hours on a hot summer day. Chlorine had been placed

14、in the pool at 8 am. Their results were as follows.MorningAfternoonTime91011121234Chlorine concentration(ppm)5.03.82.92.21.61.20.90.71.Use the calculator to find the relationship between the chlorine concentration and the time elapsed since the chlorine was placed in the pool.2.Use the results to fi

15、nd the concentration that would be needed at 8 am on a similar day to ensure that the chlorine concentration did not fall below 1.5ppm (parts per million) before 3 pm.3.If two chlorine doses were used , one at 8 am and another at 12 noon, what concentrations would be needed at these times to ensure

16、that the concentration did not fall below 1.5 ppm before 3 pm.4.What are the implication of your answers for the effective chlorination of pools at lowest cost?1. If the concentration of chlorine have been placed at the beginning is m ppm, whats the concentration of chlorine after t hours? 如果一开始投入m

17、ppm 氯，那么t hours 氯的浓度为多少？2.Use the results to find the concentration that would be needed at 8 am on a similar day to ensure that the chlorine concentration did not fall below 1.5ppm(parts per million) before 3 pm. 一开始需要投入多少浓度的氯，才能确保3pm 前氯的浓度不低于1.5ppm 3.What concentration would be needed at 8 am that

18、 the concentration did not fall below 1.5 ppm before 12 noon? 一开始需要投入多少浓度的氯，才能确保12 noon 前氯的浓度不低于1.5ppm 4.If two chlorine doses were used , one at 8 am and another at 12 noon, what concentrations would be needed at these times to ensure that the concentration did not fall below 1.5 ppm before 3 pm. 两

19、次分别需要投入多少浓度的氯，才能确保3pm前氯的浓度不低于1.5ppm1. If the concentration of chlorine have been place at the beginning is m ppm, whats the concentration of chlorine after t hours? 如果一开始投入m ppm 氯，那么t hours 氯的浓度为多少？tmey28. 02.Use the results to find the concentration that would be needed at 8 am on a similar day to

20、ensure that the chlorine concentration did not fall below 1.5ppm(parts per million) before 3 pm. 一开始需要投入多少浓度的氯，才能确保3pm 前氯的浓度不低于1.5ppm 7t728. 05 . 1 meppmem115 . 1728. 0The concentration of chlorine is 11ppm. 3.What concentration would be needed at 8 am that the concentration did not fall below 1.5 ppm before 12 noon? 一开始需要投入多少浓度的氯，才能确保12 noon 前氯的浓度不低于1.5ppm 4t428. 05 . 1 meppmem6 . 45 . 1428. 0The concentration of chlorine had been placed is 4.6ppm。 4.