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∻ ⚹ 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. ⚹◊How can the relationship between temperature and the growth rate of blue-green algae be represented in a biological context?⍭ Generate me a similar question◊

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