Question

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?
please show your steps

Answer 1

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
Answer:
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