题目内容
某医药研究所开发一种新药,据监测,如果成人按规定剂量服用该药,服药后每毫升血液中的含药量
与服药后的时间
之间近似满足如图所示的曲线.其中
是线段,曲线段
是函数![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201675169.png)
是常数
的图象.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240252017224268.jpg)
(1)写出服药后每毫升血液中含药量
关于时间
的函数关系式;
(2)据测定:每毫升血液中含药量不少于
时治疗有效,假若某病人第一次服药为早上
,为保持疗效,第二次服药最迟是当天几点钟?
(3)若按(2)中的最迟时间服用第二次药,则第二次服药后再过![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201784290.png)
,该病人每毫升血液中含药量为多少
?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201628549.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201644476.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201659378.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201659396.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201675169.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201690952.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201706241.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240252017224268.jpg)
(1)写出服药后每毫升血液中含药量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201737315.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201753271.png)
(2)据测定:每毫升血液中含药量不少于
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201768535.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201784401.png)
(3)若按(2)中的最迟时间服用第二次药,则第二次服药后再过
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201784290.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201800319.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201815373.png)
(1)
;(2)上午
;(3)
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240252018311600.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201846357.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201862678.png)
试题分析:(1)注意观察图形,区分清楚每一段图形所表示的函数表达式;(2)显然第二次服药时间应该在第二段曲线上,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201878337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201893318.png)
试题解析:(1)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201893448.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201909493.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201924359.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201940758.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201956584.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201971777.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025202018952.png)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240252018311600.png)
(2)设第一次服药最迟过
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201753271.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240252021271123.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025202143366.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025202158386.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201846357.png)
(3)第二次服药
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201784290.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025202205319.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240252022211192.png)
含第二次所服的药量为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240252022361161.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025202252777.png)
故该病人每毫升血液中的喊药量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025201862678.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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