Question #9b9bf

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Question #9b9bf

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Answer 1 · 2017-08-06T14:48:26

$29 flies$ $"29 flies"$

Explanation:

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

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

Here $x$ $x$ 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

$s (x) = 3 x + 2$ $s(x) = 3x + 2$

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

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

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

$p (3) = 5 \cdot 8 = 40$ $p(3) = 5 * 8 = 40$

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

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

$s (3) = 3 \cdot 3 + 2 = 11$ $s(3) = 3 * 3 +2 = 11$

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

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

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Question #9b9bf

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