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
15 flies
I think I choice C as my answer not sure A correct
To find the population of flies after two weeks with the spider, we need to calculate the difference between the number of flies that multiplied over two weeks and the number of flies consumed by the spider over the same period.
First, let's calculate the population of flies after two weeks without the spider by using the given function p(x) = 2(4)^x.
p(x) = 2(4)^x
p(2) = 2(4)^2
p(2) = 2(16)
p(2) = 32
So, the population of flies after two weeks without the spider is 32.
Now, let's calculate the number of flies consumed by the spider over two weeks by using the given function s(x) = 2x + 5.
s(x) = 2x + 5
s(2) = 2(2) + 5
s(2) = 4 + 5
s(2) = 9
So, the spider consumes 9 flies over two weeks.
To find the population of flies after two weeks with the spider, we subtract the number of flies consumed by the spider from the population of flies without the spider.
Population with spider = Population without spider - Flies consumed by spider
Population with spider = 32 - 9
Population with spider = 23
Therefore, the population of flies after two weeks with the introduced spider is 23 flies.