A science experiment begins with a bacterial population of 12. After 1 hour, the population is 18. After 2 hours, the population is 27.

The first thing you should do is calculate how much is the percentage of growth per hour.
 For this, we make the following rule of three:
 12 ---> 100%
 18 ---> x
 We clear x:
 x = (18/12) * (100)
 x = 150%
 Therefore, the population increases by 50% every hour.
 We now look for the function that models this problem:
 y = A (b) ^ x
 Where:
 y = total population
 A = initial population
 b = exchange rate
 x: time (in hours, in this case)
 Substituting values:
 y = 12 * (1.5) ^ x
 Let's check for 2 hours (x = 2):
 y = 12 * (1.5) ^ 2
 y = 27
 Which is correct
 Answer: 
 The function that models the problem is: 
 y = 12 * (1.5) ^ x