Multiple choice

It is given that k = x2 - 2x. If x increases by 10%, what is the percentage change in k?

  1. 10%

  2. 20%

  3. 21%

  4. Cannot be determined

  5. 0%
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D Correct answer
Explanation

If x changes to 1.1x, then k becomes (1.1x)^2 - 2(1.1x) = 1.21x^2 - 2.2x. The change in k depends on the initial value of x, so it cannot be determined as a fixed percentage.

AI explanation

The percentage change in a formula depends on the initial value of the variable, a principle known as elasticity. If x increases by 10%, the new value of k is (1.1x)^2 - 2(1.1x), which equals 1.21x^2 - 2.2x. The change in k is (1.21x^2 - 2.2x) - (x^2 - 2x), resulting in 0.21x^2 - 0.2x. Because this change depends entirely on the unknown starting value of x, a single percentage change cannot be determined.

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