Apopulation of flies grows according to the function p(x) = 3(2)x, where x is measured in weeks. a local spider has set up shop and consumes flies according to the function s(x) = 2x + 4. what is the population of flies after three weeks with the introduced spider? 10 flies

12 flies

14 flies

24 flies

The answer is 14 flies 

1. Calculate the population of flies after 3 weeks without the spider: p(3)
2. Calculate the number of eaten flies by the spider after 3 weeks: s(3)
3. Subtract p(3) and s(3) to get  the population of flies after three weeks with the introduced spider.

1. Calculate the population of flies after 3 weeks without the spider:
     p(x) = 3(2)ˣ
     x = 3 (because it is the period of three weeks)
⇒  p(3) = 3 · 2³ = 3 · 8
     p(3) = 24

2. Calculate the number of eaten flies by the spider after 3 weeks:
      s(x) = 2x + 4
      x = 3 (because it is the period of three weeks)
⇒   s(3) = 2 · 3 + 4 = 6 + 4
      s(3) = 10

3. Subtract p(3) and s(3) to get  the population of flies after three weeks with the introduced spider:
    p(3) - s(3) = 24 - 10 = 14
Therefore, there are 14 flies after three weeks with the introduced spider.