Multiple choice

The approximate value of $(1.0002)^{3000}$ is

  1. 1.2

  2. 1.4

  3. 1.6

  4. 1.8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the binomial approximation (1 + x)^n is approximately 1 + nx for small x. Here, (1 + 0.0002)^3000 is approximately 1 + (3000 * 0.0002) = 1 + 0.6 = 1.6.

AI explanation

Use the standard limit approximation formula for (1 plus small change) raised to a large power, which simplifies to 1 plus the product of the change and the power. Here, the expression is (1 plus 0.0002) to the power of 3000, so multiply 0.0002 by 3000 to get 0.6. Adding this to 1 yields a final approximate value of 1.6.

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