In a newly established wildlife reserve, $100$ rabbits are introduced into an area with an estimated carrying capacity of $10,000$ rabbits. A logistic model of the rabbit population is given by $R(t) = \frac{1,000,000}{100 + 9900 e^{-0.3t}}$, where $t$ is measured in years. Determine the time when the population reaches $6,000$ rabbits. Also, find the time when the population reaches $90\%$ of the carrying capacity. Round the final answer to the nearest integer.

The time when the population reaches $6,000$ rabbits is approximately $27\text{ years}$.

The time when the population reaches $90\%$ of the carrying capacity ($9,000$ rabbits) is approximately $33\text{ years}$.

The time when the population reaches $6,000$ rabbits is approximately $17\text{ years}$.

The time when the population reaches $90\%$ of the carrying capacity ($9,000$ rabbits) is approximately $23\text{ years}$.

The time when the population reaches $6,000$ rabbits is approximately $23\text{ years}$.

The time when the population reaches $90\%$ of the carrying capacity ($9,000$ rabbits) is approximately $17\text{ years}$.

The time when the population reaches $6,000$ rabbits is approximately $33\text{ years}$.

The time when the population reaches $90\%$ of the carrying capacity ($9,000$ rabbits) is approximately $27\text{ years}$.