x is an integer greater than 1. Quantity A: 3x+1 Quantity B: 4x

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问题 x is an integer greater than 1.
Quantity A: 3^x+1
Quantity B: 4^x

选项 A、Quantity A is greater.
B、Quantity B is greater.
C、The two quantities are equal.
D、The relationship cannot be determined from the information given.

答案D

解析我们可以直接代入几组较小的数字来确定当x=2，3^x+1=27，4^x=16，A＜B: 当x=3，3^x+1=81，4^x=64，A＜B；当x=4，3^x+1=243，4^x=256，A＞B；所以答案为D选项。这里Quantity A和B都可以看作是指数函数，底数越大，每多乘一次，上涨速度就会越快。若x取较大的值，4^x必然会大于3^x×3(即3^x+1)。那么荐考虑，当x取一个比较小的值的时候，它是大于还是小于，即可判断出最后答案。

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