To solve this problem, we must first understand the parameters of the scenario.
We know that the initial population of foxes is 40. We also know that this population triples, or increases by a factor of 3, every 15 years. This growth is represented by the equation Y = 40 * (3^X), where Y represents the future population size, 40 is the initial population size, 3 is the growth rate, and X is the number of 15-year periods.
Given that we want to know the population size after 30 years, we first need to calculate the number of 15-year periods in 30 years. By dividing 30 by 15, we find that X, the number of 15-year periods, equals 2.
We then plug X into our equation, so Y = 40 * (3^2). Here we raise 3 to the power of 2 to get 9, and then multiply this by the initial population of 40. This gives us the future population size after 30 years, Y, which is 360 foxes.
Thus, in 30 years, or 2 periods of 15 years, the fox population in the wildlife preserve will increase to 360 foxes.