Solve the Problem $P ( t )$ Decreases by Half Every $5 \mathrm { hr }$

Multiple Choice

Solve the problem.
-Eight million E. coli bacteria are present in a laboratory culture. An antibacterial agent is introduced and the population of bacteria $P ( t )$ decreases by half every $5 \mathrm { hr }$ . The population can be represented by $P ( t ) = 8,000,000 \left( \frac { 1 } { 2 } \right) ^ { t / 5 }$ . Convert this to an exponential function using base $e$ .

A) $P ( t ) = 8,000,000 e ^ { - 0.13863 t }$
B) $P ( t ) = 4,000,000 e ^ { - 0.13863 t }$
C) $P ( t ) = 8,000,000 e ^ { - 0.1 t }$
D) $P ( t ) = 4,000,000 e ^ { - 0.1 t }$