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 will it take for the fish population to reach $4000$?

• A. About $112.28\text{ hours}$
• B. About $96.32\text{ hours}$
• C. About $103.73\text{ hours}$
• D. About $72.71\text{ hours}$

Answer: (C)