Question

Biology

Posted 3 months ago

```
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?
```

Sign in to unlock the answer

Answer from Sia

Posted 3 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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question