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. 800
• B. 1600
• C. 3200
• D. 400