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
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.
