Carcass wrote:
\(x > 1\)
Quantity A |
Quantity B |
\(5^x +1\) |
\(6^x\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Given that \(x > 1\), we need to compare:
Quantity A: \(5^x + 1\)
Quantity B: \(6^x\)
\(5^x + 1\) VS \(6^x\)
Divide both sides by \(5^x\):
\((5^x + 1)/5^x\) VS \(6^x/5^x\)
Or \((1 + 1/5^x)\) VS \((6/5)^x\)
Or \((1 + 1/5^x)\) VS \((1 + 1/5)^x\)
The term \((1 + 1/5)^x\) can be expanded using binomial expansion to get: \(1^x + ... \) (many terms in-between) \( ... + (1/5)^x\)
Thus, Quantity B is greater than Quantity A
Answer B
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