The population of the colony of rabbits can be modeled by the following equation:
P(t) = 15 * b^t
where P(t) is the population of the colony at time t, and b is the growth factor.
We know that after 5 years, the population is 360 rabbits. Solving for b, we get:
360 = 15 * b^5
b^5 = 24
b = 2
Therefore, the growth factor is 2. This means that the population of the colony doubles every 5 years.
To find the population of the colony after t years, we can plug in t into the equation:
P(t) = 15 * 2^t
For example, after 10 years, the population of the colony will be:
P(10) = 15 * 2^10 = 1024
So, the population of the colony of rabbits will reach 1024 rabbits after 10 years.