Question

A bacteria culture has an initial population of 600. After 4 hours the population has grown to 1200. Assuming the culture grows at a rate proportional to the size of the population, find the function representing the population size after t hours and determine the size of the population after 8 hours.

Answer 1

Use
amount = a e^(kt) where a is the initial value, k is a constant, and t is in hours

1200 = 600 e^(k(4)
2 = e^(4k)
4k = ln 2
k = ln2 /4

amount = 600 e^((ln2/4)t)

when t=8
amount = 600 e^(2ln2)
= 2400

well, duh
Since the doubling period seems to be 4 hours
in 8 hours they would have doubled twice
600 --> 1200 --> 2400