Food webs and energy pyramids show the movement of matter and energy through ecosystems. 16. Click to show how matter and energy move through ecosystems.

flows through the ecosystem____

cycles within the ecosystem ____

Earth has a generally fixed amount ____

Earth is always receiving more ____

5 answers

In ecosystems, the movement of matter and energy can be described in the following ways:

Energy flows through the ecosystem: Energy primarily enters an ecosystem through sunlight, which is captured by producers (like plants) in the process of photosynthesis. This energy is then transferred through various trophic levels (primary consumers, secondary consumers, etc.) as organisms consume one another. However, energy is lost at each trophic level, mainly as heat, according to the second law of thermodynamics.

Matter cycles within the ecosystem: Unlike energy, matter (such as nutrients) is recycled within an ecosystem. Matter cycles through biogeochemical cycles, such as the water cycle, carbon cycle, and nitrogen cycle. This allows elements and compounds to be reused and repurposed by different organisms continuously. Decomposers play a critical role in breaking down dead organic matter, returning vital nutrients to the soil for producers to use again.

Earth has a generally fixed amount of matter: The total amount of matter on Earth remains relatively constant over time. Elements like carbon, nitrogen, and phosphorus are reused and cycled through different forms and locations in the ecosystem.

Earth is always receiving more energy: While matter is finite and cycles within ecosystems, energy (especially from the sun) is continuously received by the Earth. This incoming solar energy drives the processes and interactions that occur within ecosystems, allowing them to sustain life.

Overall, these concepts highlight the differences between the flow of energy (which is linear and one-way) and the cycling of matter (which is circular and transformative) in ecosystems.

The library needs at least 15 people to sign up for an event in order to run it. Currently, 3 people have signed up, and the library expects 2 more people to sign up each day. After how many days will the library be sure it can run the event? Write an inequality that could be used to solve this problem.

To determine after how many days the library will be sure it can run the event, we can set up the following inequality.

Let \( d \) represent the number of days until the event. Since 3 people have already signed up and the library expects 2 more people to sign up each day, the total number of people signed up after \( d \) days can be expressed as:

\[ 3 + 2d \]

The library needs at least 15 people to run the event, so we can set up the inequality:

\[ 3 + 2d \geq 15 \]

Now, let's solve the inequality:

  1. Subtract 3 from both sides: \[ 2d \geq 12 \]

  2. Divide both sides by 2: \[ d \geq 6 \]

Therefore, after 6 days, the library will be sure that at least 15 people have signed up to run the event.

Ellie is saving to buy a phone. She wants to have at least $299 saved before buying one. She currently has $213 saved, and she receives $10 a week as an allowance from her parents. After how many weeks will Ellie have enough money saved? Ellie writes the inequality 10w+213≥299, where w is the number of weeks, to help figure this out. Solve her inequality.

w≥86

w86≥860

w860≥8.6w

w8.6≥51.2

Let's solve the inequality that Ellie wrote, which is:

\[ 10w + 213 \geq 299 \]

  1. Subtract 213 from both sides: \[ 10w \geq 299 - 213 \] \[ 10w \geq 86 \]

  2. Divide both sides by 10: \[ w \geq \frac{86}{10} \] \[ w \geq 8.6 \]

Since \( w \) represents the number of weeks and must be a whole number, we round up to the nearest whole number, which means Ellie needs at least 9 weeks to have enough money saved.

The inequality that Ellie wrote has been solved correctly, and the key result is:

\[ w \geq 8.6 \]

Therefore, the correct interpretation of how many weeks Ellie needs is 9 weeks.

There seems to be some confusion with the choices you provided, as none of them directly reflect the solution we found. The correct answer based on our calculations is:

\[ w \geq 9 \]