(4分)记水的质量为$d=\dfrac{S-1}{\ln n}$,并且$d$越大,水质量越好.若$S$不变,且$d_{1}=2.1$,$d_{2}=2.2$,则$n_{1}$与$n_{2}$的关系为( ) A.$n_{1} < n_{2}$ B.$n_{1} > n_{2}$ C.若$S < 1$,则$n_{1} < n_{2}$;若$S > 1$,则$n_{1} > n_{2}$ D.若$S < 1$,则$n_{1} > n_{2}$;若$S > 1$,则$n_{1} < n_{2}$ 答案:$C$ 分析:根据已知条件,推得$\left\{\begin{array}{l}{{n}_{1}={e}^{\dfrac{S-1}{2.1}}}\\ {{n}_{2}={e}^{\dfrac{S-1}{2.2}}}\end{array}\right.$,再结合$S$的大小,以及指数函数的单调性,即可求解. 解:水的质量为$d=\dfrac{S-1}{\ln n}$,$d_{1}=2.1$,$d_{2}=2.2$, 则$\left\{\begin{array}{l}{{d}_{1}=\dfrac{S-1}{\ln {n}_{1}}=2.1}\\ {{d}_{2}=\dfrac{S-1}{\ln {n}_{2}}=2.2}\end{array}\right.$,解得$\left\{\begin{array}{l}{{n}_{1}={e}^{\frac{S-1}{2.1}}}\\ {{n}_{2}={e}^{\frac{S-1}{2.2}}}\end{array}\right.$, 若$S > 1$, 则$\dfrac{S-1}{2.1} > \dfrac{S-1}{2.2}$, $y=e^{x}$在$R$上单调递增, 所以$n_{1} > n_{2}$, 若$S=1$,则$\dfrac{S-1}{2.1}=\dfrac{S-1}{2.2}=0$, $y=e^{x}$在$R$上单调递增, 所以$n_{1}=n_{2}=1$; 若$S < 1$,则$\dfrac{S-1}{2.1} < \dfrac{S-1}{2.2}$, $y=e^{x}$在$R$上单调递增, 所以$n_{1} < n_{2}$, 结合选项可知$C$正确,$ABD$错误. 故选:$C$. 点评:本题主要考查函数的实际应用,考查转化能力,属于中档题.
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