Final answer:
The pattern where the number of mice triples each year is represented by an exponential growth function, specifically in the form of P * 3^n where P is the starting population and n is the number of years.
Step-by-step explanation:
The pattern you're describing, in which the number of mice triples each year, is best represented by an exponential growth function. This type of function displays rapid growth over time because the rate of growth is proportional to the current size of the population. In other words, as the population increases, the rate of growth increases as well.
If the number of mice at the start (year 0) is denoted as P, and n is the number of years passed, then the function representing the population growth would be P * 3^n. This equation shows when we increase n by one year, the population triples.
It's worth noting that this model is a simplification and doesn't consider factors like resources limitations or changes in environment that usually lead the population growth to slow down and level off to zero at some point. That scenario is better represented by a logistic growth model.
Learn more about Exponential Growth