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