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1 . 某科创公司新开发了一种溶液产品,但这种产品含有
的杂质,按市场要求杂质含量不得超过
,现要进行过滤,已知每过滤一次杂质含量减少
,要使产品达到市场要求,对该溶液过滤的最少次数为______ .
(参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f762a1de162d8dca6dcd06a3107c3fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe619bd93756ad8656ba0d02c4fddca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef98775e12ea3852135792e34526a519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295fbcedb830aa9acb83aef417f07202.png)
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解题方法
2 . “阿托秒”是一种时间的国际单位,“阿托秒”等于
秒,原子核内部作用过程的持续时间可用“阿托秒”表示.《庄子・天下》中提到,“一尺之棰,日取其半,万世不竭”,如果把“一尺之棰”的长度看成1米,按照此法,至少需要经过______ 天才能使剩下“棰”的长度小于光在2“阿托秒”内走过的距离.(参考数据:光速为
米/秒,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4554dce3433acf5ce7fe4c8d3d6e4850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805f1572ef236a01de00982c69130bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769563348a6488d1db86b5b4c7681644.png)
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2024高三·全国·专题练习
3 . 某食品的保鲜时间
(单位:小时)与储存温度
(单位:
)满足函数关系
(
为自然对数的底数,
为常数).若该食品在0
的保鲜时间设计192小时,在22
的保鲜时间是48小时,则该食品在33
的保鲜时间是_____ 小时.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36e598994b6f7c694f5f20daebb8762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1430782849401cf3c2ea8a49afacda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb91abeed60da0f999b46e337957dec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de96374212b9a5df820d78d10e7d1291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de96374212b9a5df820d78d10e7d1291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de96374212b9a5df820d78d10e7d1291.png)
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4 . 把物体放在冷空气中冷却,如果物体原来的温度是
,空气的温度是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18c9583db613005922ec8d316ee94d3.png)
后物体的温度可由公式
求得,且把温度是
的物体放在
的空气中冷却
后,物体的温度是
,那么
的值约等于______ .(保留一位小数)(参考数据:
取1.099,
取0.693)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2456350210a7ed02daeb0010abc376a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18c9583db613005922ec8d316ee94d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f67e1147d0df6c52b45be0d2f8da090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962d6068a75a376f8487de79d4cbd80a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6cca692e47077db0c89675b1beb4847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c534228d6a812977052bc1afa5a95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cec183057249005d5f234c4bea5de7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866116aa168650d791609535627e3cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e24d42f61784c642e9eb1316afdd2ad.png)
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5 . Logistic模型是常用数学模型之一,可应用于流行病学领域,有学者根据公布数据建立了某地区新冠肺炎累计确诊病例数
(
单位:天)的Logistic模型:
,其中
为最大确诊病例数.当
时,标志着已初步遏制疫情,则
约为______ 天.(注:
为自然对数的底数,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79994f2c805ec5b31af3756bbc159113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702668bc333781961c75e4703990f719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d7d88ec306b3fdb3ad8db7c3471a0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f25f3ddde85835984b2f387e91ece7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee623d144a8ba70650e0e9c44ca1d8e6.png)
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2024高三·全国·专题练习
6 . 某食品的保鲜时间
(单位:小时)与储藏温度
(单位:
满足函数关系
为自然对数的底数,
为常数).若该食品在
的保鲜时间是192小时,在
的保鲜时间是48小时,则该食品在
的保鲜时间是__ 小时.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49d34e483a1002ae389635e86e2c2ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4cb11cfe0dcd5e2894cc6e29bc8b6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceee0ff5c929d67de3c294e027c9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644a7a82d8e238066fc4590deb7ebda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe0fcd9e2925ecad7064f8fbbce145b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdba55218e9cbb10b85295e5869a9ab5.png)
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7 . 中国茶文化源远流长,博大精深,茶水的口感与茶叶的类型和水的温度有关,某种绿茶用
的水泡制,再等到茶水温度降至
时饮用,可以产生最佳口感.为了控制水温,某研究小组联想到牛顿提出的物体在常温下的温度变化冷却规律:设物体的初始温度是
,经过
后的温度是T,则
,其中
表示环境温度,h为常数.该研究小组经过测量得到,刚泡好的绿茶水温度是
,放在
的室温中,
以后茶水的温度是
,在上述条件下,大约需要再放置__________
能达到最佳饮用口感.(结果精确到0.1,参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13708f01d71b3172e2508af0d620572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7158d8fec00479a56aa0333f550a92d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635ccd929471d564cc9d2d96266b34d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5481d5a5e5f293cb87ce8d5be068097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a3fec95b58468366bd7f9d965b3db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232519a6b38ae0975ef2e2f8f6f34488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13708f01d71b3172e2508af0d620572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ccac4181d8a1fe89f03c89ca7c42fe.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6bef2cb190a95c42e08f15db588320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e008ee8b0dc593ce21d8d4c87afef1c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50101047632b94dcd5cf8035b093cc5.png)
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2024-03-08更新
|
111次组卷
|
2卷引用:安徽省A10联盟2023-2024学年高一下学期开学考试数学试卷
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8 . 某杀菌剂每喷洒一次就能杀死某物质上的细菌的
,要使该物质上的细菌少于原来的
,则至少要喷洒______ 次
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceceedf836ef596f48d5bd2313714151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb30e2572976018360c3cbf6976a472d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1732beb04467d20afa249f876ee7d77.png)
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9 . 冰箱,空调等家用电器使用了氟化物,氛化物的释放破坏了大气上层的臭氧层,使臭氧含量
呈指数函数型变化,在氟化物排放量维持某种水平时,具有关系式
,其中
是臭氧的初始量,
是自然对数的底数,
,试估计______ 年以后将会有一半的臭氧消失.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2912b65a975a1d91d59073f2ac24d06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1698b9a76d725f9a254b9798d926fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7753227327ac93a1df75c262e575c16.png)
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10 . 表观活化能的概念最早是针对Arrhenius(阿伦尼乌斯)公式
中的参量
提出的,是通过实验数据求得,又叫实验活化能,Arrhenius公式中的k为反应速率常数,
为摩尔气体常量,
为热力学温度(单位为开尔文,简称开),
为阿伦尼乌斯常数.已知某化学反应的温度每增加
开,反应速率常数
变为原来的
倍,则当温度从
开上升到
开时,
=______ .(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd97cbdff30dce1a4419c56bbb9cbed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86722368bfcb473b7fbfa20053de93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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