Multiple choice

The approximate value of $(1.01)^{-7}$ is

  1. $0.3$
  2. $0.7$
  3. $0.49$
  4. $0.93$
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D Correct answer
Explanation

Using the binomial approximation (1 + x)^n approx 1 + nx for small x, (1 + 0.01)^(-7) approx 1 + (-7)(0.01) = 1 - 0.07 = 0.93.

AI explanation

Using the first order linear approximation for exponents, 1 plus x raised to the power of negative n is approximately 1 minus nx for small values of x. Here x equals 0.01 and n equals 7, so the expression is approximately 1 minus 7 multiplied by 0.01. This calculates to 0.93.

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