$\"\"$

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Population P of bacteria in a sample after t days is $\"\"$ .

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Apply derivative to function $\"\"$ .

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$\"\"$

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Find maximum and minimum values equate $\"\"$ .

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$\"\"$

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$\"\"$ and $\"\"$ .

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Draw a table to determine the nature of the function:

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Test interval	x - value	Inequality	Conclusion
$\"\"$	$\"\"$	$\"\"$	Decreasing
$\"\"$	$\"\"$	$\"\"$	Increasing
$\"\"$	$\"\"$	$\"\"$	Decreasing

\

$\"\"$

\

a.

\

Every cubic function is a polynomial.

\

So the function $\"\"$ is a polynomial.

\

b.

\

The function is increasing over the interval $\"\"$ .

\

c.

\

The function is Decreasing over the interval $\"\"$ .

\

$\"\"$

\

a.

\

Every cubic function is a polynomial.

\

So the function $\"\"$ is a polynomial.

\

b.

\

The function is increasing over the interval $\"\"$ .

\

c.

\

The function is Decreasing over the interval $\"\"$ .