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82% (00:54) correct
17% (02:08) wrong based on 104 sessions
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\(2^n + 2^n + 2^n + 2^n = 4^{n+3}\)
Quantity A
Quantity B
n
4
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
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
--------ASIDE------------------------ Many students will fail to correctly simplify the terms on the left side of the given equation. Notice that k + k + k + k = 4k And x² + x² + x² + x² = 4x² And 2m + 2m + 2m + 2m = 4(2m) = 8m Likewise, \(2^n + 2^n + 2^n + 2^n = 4(2^n)\) -----ONTO THE QUESTION!!---------------
GIVEN: \(2^n + 2^n + 2^n + 2^n = 4^{n+3}\)
Simplify left side: \(4(2^n) = 4^{n+3}\)
Rewrite both 4's as follows: \((2^2)(2^n) = (2^2)^{n+3}\)
Simplify both sides: \(2^{2+n} = 2^{2n+6}\)
Since we now have the same base on each side, we can conclude that: \(2+n = 2n+6\)
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.