Question

ecosystem dynamics practice
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part 1: the 10% rule practice
in an ecosystem, only about 10% of the energy from one trophic level is transferred to the next. solve the following problems to understand how energy moves up the food chain.

1. a flower has 5,000 units of energy. how much energy is available to the primary consumer?
2. if a primary consumer receives 500 units of energy from eating plants, how much energy is available to the secondary consumer?
3. a secondary consumer eats an organism that has 100 units of energy. how much energy will the tertiary consumer receive?
4. if a hawk at the top of the food chain has 1 unit of energy available, how much energy did the producer start with?
5. a grasshopper consumes a plant that has 3,750 units of energy. how much energy is available to the frog that eats the grasshopper?
6. a wolf at the top of the food chain receives 2.3 joules of energy. how much energy did the producer originally have?

Explanation:

Step1: Calculate energy transfer

Use the formula \(E_{next}=E_{current}\times10\%\) (where \(E_{next}\) is energy for next trophic level and \(E_{current}\) is current energy).

Step2: Solve each problem

1. For the flower (producer) with \(E = 5000\) units, energy to primary consumer: \(5000\times0.1=500\) units.
2. Primary consumer has \(E = 500\) units, energy to secondary consumer: \(500\times0.1 = 50\) units.
3. Secondary consumer has \(E = 100\) units, energy to tertiary consumer: \(100\times0.1=10\) units.
4. Let producer energy be \(x\). After three - level transfer (\(x\times0.1\times0.1\times0.1 = 1\)), so \(x=\frac{1}{0.1\times0.1\times0.1}=1000\) units.
5. Plant has \(E = 3750\) units (grasshopper is primary consumer), energy to frog (secondary consumer): \(3750\times0.1\times0.1 = 37.5\) units.
6. Let producer energy be \(y\). After three - level transfer (\(y\times0.1\times0.1\times0.1=2.3\)), so \(y=\frac{2.3}{0.1\times0.1\times0.1}=2300\) Joules.

Answer:

1. \(500\) units
2. \(50\) units
3. \(10\) units
4. \(1000\) units
5. \(37.5\) units
6. \(2300\) Joules