If a Bacteria Population Starts with 100 Bacteria and Doubles $n=f(t)=100\left(2^{\frac{t}{3}}\right)$

Multiple Choice

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is $n=f(t) =100\left(2^{\frac{t}{3}}\right)$ . When will the population reach 35,000? Round the answer to the nearest tenth.

A) 30.4 hours
B) 15.4 hours
C) 20.4 hours
D) 35.4 hours
E) 25.4 hours