A population of flies grows according to the function p (x) = 6 (3) ^x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s (x) = 4x+1. What is the population of the flies after two weeks with the introduced spider?

The final population of the flies is equal to the growth rate minus the number of flies consumed by the spiders. That is,

final population = 6 (3^x) - (4x + 1)

Substituting 2 to the x of the equation above,

final population = 6 (3²) - (4 (2) + 1) = 45

Thus, the final population of the flies would be 45.