A certain species of fish in a lake reproduces at a rate that doubles its population every $24~\text{hours}$. The initial population of the fish was $200$. If the population $t$ hours after the initial observation is represented by the function $p\left(t\right)=200\cdot{2^{\frac{t}{24}}}$, what would be the population $3~\text{days}$ after the initial observation?

A certain species of fish in a lake reproduces at a rate that doubles its population every $24~\text{hours}$. The initial population of the fish was $200$. If the population $t$ hours after the initial observation is represented by the function $p\left(t\right)=200\cdot{2^{\frac{t}{24}}}$, how long does it take for the fish population to quadruple?

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.