Question

Biology

Posted 5 months ago

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When warm water is released into a river from a source such as a power plant, the increased temperature of the water causes some algae to grow and other algae to die. In particular, bluegreen algae can be toxic to some aquatic life. If $g(t)$ organisms/hour per ${ }^{\circ} \mathrm{C}$ is the rate of change of the growth rate of blue - green algae and $t$ is the temperature of the water in ${ }^{\circ} \mathrm{C}$, what does the area of the region between the graph of $g$ and the $t$ - axis from $t=25^{\circ} \mathrm{C}$ to $t=35^{\circ} \mathrm{C}$ represent?
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Answer from Sia

Posted 5 months ago

Answer

The area represents the total change in the number of blue-green algae organisms over the temperature range from $25^{\circ} \mathrm{C}$ to $35^{\circ} \mathrm{C}$.

Solution

a

Interpretation of the integral: The area under the curve of a rate function over a given interval represents the total amount of change over that interval

b

Application to the given problem: In this context, the area between the graph of $g(t)$ and the $t$-axis from $t=25^{\circ} \mathrm{C}$ to $t=35^{\circ} \mathrm{C}$ represents the total change in the growth rate of blue-green algae organisms per hour per degree Celsius over the 10-degree temperature range

Key Concept

Integral of a rate of change

Explanation

The integral of a rate function over a specific interval gives the net change in the quantity being measured over that interval. In this case, it is the net change in the number of blue-green algae organisms with respect to the water temperature.

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