The approximate value of ^{3000} \) is

Using the binomial expansion (1+x)^n ≈ 1 + nx for small x, we get (1.0002)^3000 ≈ 1 + 3000×0.0002 = 1.6. However, since nx = 0.6 is not extremely small, a better approximation uses the exponential: (1.0002)^3000 ≈ e^{3000×ln(1.0002)} ≈ e^{0.6} ≈ 1.822. The closest option is 1.8. Alternatively, including the second-order term n(n-1)x^2/2 gives about 0.18, so total ≈ 1.78, again closest to 1.8.