Question

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?

Answer 1

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.