Question

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?

Answer 1

The functions are:

$p(x)=2\cdot4^x$ and $s(x)=2x+5$.

After 2 weeks, under no risk of spiders, the population of the flies is calculated by the function as $p(2)=2\cdot4^2=2\cdot16=32$.

 
Similarly, we calculate s(2)=2(2)+5=4+5=9, which means that the spider consumes 9 flies in 2 weeks.

 
Thus, out of 32 flies, 9 are eaten by the spider, so there are 32-9=23 flies left. 


Answer: 23