The number of radioactive nuclei $$N$$ of a radioactive sample is experimentally measured as a function of time $$t$$. At $$t=0$$, $$N=50000$$ and at $$t=10\ \text{s}$$, $$N=5000\pm100$$. The half-life of the sample is estimated from these measurements. The error in the estimation of the half-life is approximately. For small $$x$$, use $$\ln(1+x)\approx x$$.

A

$$0.26\ \text{s}$$

B

$$0.15\ \text{s}$$

C

$$0.05\ \text{s}$$

D

$$0.10\ \text{s}$$