A bacteria culture starts with 200 bacteria and triples in size every half hour. The population of the bacteria after $t$ hours is:
A) $200 \left( 9 ^ { - t } \right)$
B) $200 \left( 9 ^ { t } \right)$
C) $200 \left( 3 ^ { - t } \right)$
D) $200 \left( 3 ^ { t } \right)$
E) $200 \left( e ^ { - t } \right)$
F) $200 \left( e ^ { t } \right)$
G) $200 \left( e ^ { - 3 t } \right)$
H) $200 \left( e ^ { 3 t } \right)$

Question

A bacteria culture starts with 200 bacteria and triples in size every half hour. The population of the bacteria after $t$ hours is:
A) $200 \left( 9 ^ { - t } \right)$ 
B) $200 \left( 9 ^ { t } \right)$ 
C) $200 \left( 3 ^ { - t } \right)$ 
D) $200 \left( 3 ^ { t } \right)$ 
E) $200 \left( e ^ { - t } \right)$ 
F) $200 \left( e ^ { t } \right)$ 
G) $200 \left( e ^ { - 3 t } \right)$ 
H) $200 \left( e ^ { 3 t } \right)$

Quizplus · Accepted Answer

The population triples every half hour, so in one hour (t=1), it will triple twice. This is represented by the formula $200 \times 3^{2t}$, which simplifies to $200 \times 9^t$, matching option B.

A Bacteria Culture Starts with 200 Bacteria and Triples in Size