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