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2 years ago

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A population of flies grows according to the function p(x) = 2(4)x, where x is measured in weeks. A local spider has set up shop

and consumes flies according to the function s(x) = 2x + 5. What is the population of flies after two weeks with the introduced spider?

1 answer:

aleksandr82 [10.1K]2 years ago

7 0

The functions are:

$p(x)=2\cdot4^x$ and $s(x)=2x+5$ .

After 2 weeks, under no risk of spiders, the population of the flies is calculated by the function as $p(2)=2\cdot4^2=2\cdot16=32$ .

Similarly, we calculate s(2)=2(2)+5=4+5=9, which means that the spider consumes 9 flies in 2 weeks.

Thus, out of 32 flies, 9 are eaten by the spider, so there are 32-9=23 flies left.

Answer: 23

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<h3>Procedure - Determination of an appropriate function based on given information</h3>

In this question we must find an appropriate model for a <em>periodic</em> function based on the information from statement. <em>Sinusoidal</em> functions are the most typical functions which intersects a midline ( $x_{mid}$ ) and has both a maximum ( $x_{max}$ ) and a minimum ( $x_{min}$ ).

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$\phi$ - Angular phase, in radians.

If we know that $x_{min} = -14.5$ , $x_{mid} = -8$ , $x_{max} = -1.5$ , $(t, x) = (-\pi, -8)$ and $(t, x) = \left(\frac{\pi}{4}, -1.5 \right)$ , then the sinusoidal function is:

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The resulting system is:

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And we proceed to solve this system:

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By (2c):

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To learn more on functions, we kindly invite to check this verified question: brainly.com/question/5245372

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