求教 PREP 一道数学题

sunfish223

The rate of a certain chemical reaction is directly proportional to the square of the concentration of  chemical A present and inversely portpotional to the concentration of chemical B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
A 100% decrease
B 50%  decrease
C 40% decrease
D 40% increase
E 50% increase

答案 D 帮忙解释下哦 O(∩_∩)O谢谢

tommy8163

由于R正比于A^2,反比于B 所以 R = KA^2/B   现在B = 2B，题目要求R不变，所以（AX）^2/(2B) = A^2/B,  得到X^2 = 2 所以X = 1.414，也就是增加了 40%