Question

Question #9b9bf

Answer 1

`"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"`