Question

A population 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

Answer 1

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.