A population of flies grows according to the function p(x)=2(4)^x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x)=2x + 5. What is the population of flies after two weeks with the introduced spider?
15 flies
23 flies
32 flies
36 flies
The population of flies is given by the function (p-s)(x).
(p-s)(2) = [2(4)²] - [2(2) + 5]
(p-s)(2) = [32] - [9]
(p-s)(2) = 23
Thus, the population of the flies after 2 weeks would be 23.
To find the population of flies after two weeks with the introduced spider, we need to substitute x = 2 into the function p(x)=2(4)^x.
p(2) = 2(4)^2
p(2) = 2(16)
p(2) = 32
Therefore, the population of flies after two weeks with the introduced spider is 32 flies. Hence, the correct answer is 32 flies.
To find the population of flies after two weeks with the introduced spider, we need to evaluate the fly population function p(x) at x = 2.
The function p(x) = 2(4)^x represents the growth of the fly population over time, where x is measured in weeks.
To find p(2), we substitute x = 2 into the function:
p(2) = 2(4)^2
p(2) = 2(16)
p(2) = 32
Therefore, the population of flies after two weeks with the introduced spider is 32 flies.