Five million bacteria live in an organism. the doubling period is 1.5 hours. how many will there be after: a) t hours? b) 9 hours? c) 1 day? d) 2 hours? show your steps

We write the generic exponential equation:
 y = A (b) ^ t
 Where,
 A: initial population
 B: growth rate
 t: time in hours.
 Substituting values we have:
 y = 5 (2) ^ ((1 / 1.5) * t)
 For t = 9 hours we have:
 y = 5 (2) ^ ((1 / 1.5) * 9)
 y = 320 million
 For t = 24 hours (one day) we have:
 y = 5 (2) ^ ((1 / 1.5) * 24)
 y = 327680 million
 For t = 2 hours we have:
 y = 5 (2) ^ ((1 / 1.5) * 2)
 y = 12.5992105 million
 
 a) t hours?
 y = 5 (2) ^ ((1 / 1.5) * t)
 b) 9 hours?
 y = 320 million
 c) 1 day?
 y = 327680 million
 d) 2 hours?
 y = 12.5992105 million