Question #9b9bf

1 Answer
Aug 6, 2017

Answer:

#"29 flies"#

Explanation:

You know that the population of flies can be modeled by the function

#p(x) = 5 * 2^x#

Here #x# represents the number of weeks that pass in a given period of time.

You also know that a local spider consumes flies according to the function

#s(x) = 3x + 2#

Your goal here is to figure out the population of flies after #3# weeks, which basically means that you need to figure out how many flies are around at #x = 3#.

So, you know that after #3# weeks, you will have

#p(3) = 5 * 2^3#

#p(3) = 5 * 8 = 40#

This means that after #3# weeks, the population of flies will hit #40# individuals if no spider is present.

However, a spider is indeed present. In #3# weeks, the spider will consume

#s(3) = 3 * 3 +2 = 11#

flies. So at the end of this #3#-week period, you will be left with

#"40 flies"color(white)(.) - overbrace("11 flies")^(color(blue)("consumed by the spider")) = "29 flies"#