# Question #9b9bf

Aug 6, 2017

$\text{29 flies}$

#### Explanation:

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

$p \left(x\right) = 5 \cdot {2}^{x}$

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

$s \left(x\right) = 3 x + 2$

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

$p \left(3\right) = 5 \cdot {2}^{3}$

$p \left(3\right) = 5 \cdot 8 = 40$

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

$s \left(3\right) = 3 \cdot 3 + 2 = 11$

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

$\text{40 flies"color(white)(.) - overbrace("11 flies")^(color(blue)("consumed by the spider")) = "29 flies}$