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. Plot the graph of the derivative of $R$ and determine the year when the population is growing fastest. Round the answer to 2 decimal places.

• A. The population is growing fastest at $t\approx 30.64\text{ years}$.
• B. The population is growing fastest at $t\approx$ $32.15\text{ years}$.
• C. The population is growing fastest at $t\approx$ $17.32\text{ years}$.
• D. The population is growing fastest at $t\approx$ $15.32\text{ years}$.

Answer: (D)