Question

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

• A. 1.2
• B. 1.4
• C. 1.6
• D. 1.8

Hint:

For small \(x\), \((1+x)^n \approx 1 + nx\).

Answer 1

The Correct Option is C

Step 1: Underlying Concept:
\text{Use binomial approximation }(1+x)^n \approx 1 + nx\text{ for small }x.
Step 2: Explanation:
(1.0002)^{3000} = (1 + 0.0002)^{3000}
\approx 1 + 3000 \times 0.0002
= 1 + 0.6
= 1.6
Step 3: Conclusion:
1.6