In the 1980's the rate of increase of the minority population of the United States was nearly
twice as fast as the 1970's.
Option Elimination -
In standard usage - 1970's and the 1970s mean the same - the decade from 1970 to 1979.
(A) twice as fast as - "the rate" is compared with a decade. Moreover, "the rate" can not be faster, slower, or greater. It can be just twice something.
(B) twice as fast as it was in - "the rate" can not be faster, slower, or greater. It can be just twice something.
(C) twice what it was in - "What" can also introduce a noun clause, known as an indirect question, in which the clause functions as a noun or the object. Eg. The researcher wanted to know what the results would be. She asked me what my plans were. I was curious about what caused the problem. In the noun clauses introduced by "what" acts as an object of the verb "know," "asked," and "curious about."
The comparison is complete - In the 1980's, the rate of increase of the minority population of the United States was nearly twice what the rate of increase was in the 1970's. We could also convey the same meaning: "In the 1980's, the rate of increase of the minority population of the United States was nearly twice the rate of increase in the 1970's." But we don't have any option like this.
(D) two times faster than that of - "the rate" can not be faster, slower, or greater. It can be just twice something.
(E) two times greater than - "the rate" compared with a decade of 1970s/1970's - wrong.