# Question #9b9bf

##### 1 Answer

#### Answer:

#### Explanation:

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

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

Here *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 **weeks**, which basically means that you need to figure out how many flies are around at

So, you know that after **weeks**, you will have

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

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

This means that after **weeks**, the population of flies will hit **if no spider is present**.

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

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

flies. So at the end of this

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