Multiple choice

What is the approximate value of (1.02)8?

  1. 1.171

  2. 1.175

  3. 1.177

  4. 1.179
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A Correct answer
Explanation

Using the binomial expansion (1+x)^n = 1 + nx + n(n-1)/2 * x^2 + ..., where x=0.02 and n=8. This gives 1 + 8(0.02) + 28(0.0004) = 1 + 0.16 + 0.0112 = 1.1712, which is approximately 1.171.

AI explanation

Use the binomial expansion approximation formula (1 + x)^n is approximately 1 + nx for very small values of x. Substituting x = 0.02 and n = 8 gives 1 + (8 x 0.02), which equals 1.16. Since the choices are very close, the intended approximate value among them is 1.171, although a more precise calculation gives 1.1717.

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