Apply Math to Energy Flow - Biology
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Calculate efficiency if $E_{p} = 3600\ \text{kJ}$ and $E_{n} = 540\ \text{kJ}$.
Calculate efficiency if $E_{p} = 3600\ \text{kJ}$ and $E_{n} = 540\ \text{kJ}$.
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$15%$. Use efficiency formula: $\frac{540}{3600} \times 100% = 15%$.
$15%$. Use efficiency formula: $\frac{540}{3600} \times 100% = 15%$.
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Find the energy at the next trophic level if producers have $20000\ \text{kJ}$ and efficiency is $10%$.
Find the energy at the next trophic level if producers have $20000\ \text{kJ}$ and efficiency is $10%$.
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$2000\ \text{kJ}$. Apply $10%$ rule: $20000 \times 0.1 = 2000$.
$2000\ \text{kJ}$. Apply $10%$ rule: $20000 \times 0.1 = 2000$.
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Find energy lost if $E_{p} = 2500\ \text{kJ}$ and $E_{n} = 125\ \text{kJ}$.
Find energy lost if $E_{p} = 2500\ \text{kJ}$ and $E_{n} = 125\ \text{kJ}$.
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$2375\ \text{kJ}$. Subtract transferred from previous: $2500 - 125 = 2375$.
$2375\ \text{kJ}$. Subtract transferred from previous: $2500 - 125 = 2375$.
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How much energy remains after two $10%$ transfers starting from $10000\ \text{kJ}$?
How much energy remains after two $10%$ transfers starting from $10000\ \text{kJ}$?
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$100\ \text{kJ}$. Two $10%$ transfers: $10000 \times (0.1)^2 = 100$.
$100\ \text{kJ}$. Two $10%$ transfers: $10000 \times (0.1)^2 = 100$.
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How much energy remains after three $10%$ transfers starting from $50000\ \text{kJ}$?
How much energy remains after three $10%$ transfers starting from $50000\ \text{kJ}$?
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$50\ \text{kJ}$. Three $10%$ transfers: $50000 \times (0.1)^3 = 50$.
$50\ \text{kJ}$. Three $10%$ transfers: $50000 \times (0.1)^3 = 50$.
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How much energy remains after four $10%$ transfers starting from $200000\ \text{kJ}$?
How much energy remains after four $10%$ transfers starting from $200000\ \text{kJ}$?
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$20\ \text{kJ}$. Four $10%$ transfers: $200000 \times (0.1)^4 = 20$.
$20\ \text{kJ}$. Four $10%$ transfers: $200000 \times (0.1)^4 = 20$.
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Calculate $\text{NPP}$ if $\text{GPP} = 1500$ and producer respiration $R = 600$ (same units).
Calculate $\text{NPP}$ if $\text{GPP} = 1500$ and producer respiration $R = 600$ (same units).
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$900$. Use NPP formula: $1500 - 600 = 900$.
$900$. Use NPP formula: $1500 - 600 = 900$.
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Calculate $\text{GPP}$ if $\text{NPP} = 700$ and producer respiration $R = 300$ (same units).
Calculate $\text{GPP}$ if $\text{NPP} = 700$ and producer respiration $R = 300$ (same units).
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$1000$. Rearrange NPP formula: $700 + 300 = 1000$.
$1000$. Rearrange NPP formula: $700 + 300 = 1000$.
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Calculate producer respiration $R$ if $\text{GPP} = 2200$ and $\text{NPP} = 1600$ (same units).
Calculate producer respiration $R$ if $\text{GPP} = 2200$ and $\text{NPP} = 1600$ (same units).
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$600$. Rearrange NPP formula: $2200 - 1600 = 600$.
$600$. Rearrange NPP formula: $2200 - 1600 = 600$.
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If producers store $12000\ \text{kJ}$ as NPP, estimate energy available to primary consumers using $10%$.
If producers store $12000\ \text{kJ}$ as NPP, estimate energy available to primary consumers using $10%$.
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$1200\ \text{kJ}$. Apply $10%$ rule to NPP: $12000 \times 0.1 = 1200$.
$1200\ \text{kJ}$. Apply $10%$ rule to NPP: $12000 \times 0.1 = 1200$.
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If primary consumers have $900\ \text{kJ}$, estimate energy available to secondary consumers using $10%$.
If primary consumers have $900\ \text{kJ}$, estimate energy available to secondary consumers using $10%$.
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$90\ \text{kJ}$. Apply $10%$ rule: $900 \times 0.1 = 90$.
$90\ \text{kJ}$. Apply $10%$ rule: $900 \times 0.1 = 90$.
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If tertiary consumers have $8\ \text{kJ}$ and transfer is $10%$, what was secondary consumer energy?
If tertiary consumers have $8\ \text{kJ}$ and transfer is $10%$, what was secondary consumer energy?
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$80\ \text{kJ}$. Reverse $10%$ rule: $8 \div 0.1 = 80$.
$80\ \text{kJ}$. Reverse $10%$ rule: $8 \div 0.1 = 80$.
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If secondary consumers have $60\ \text{kJ}$ and transfer is $10%$, what was primary consumer energy?
If secondary consumers have $60\ \text{kJ}$ and transfer is $10%$, what was primary consumer energy?
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$600\ \text{kJ}$. Reverse $10%$ rule: $60 \div 0.1 = 600$.
$600\ \text{kJ}$. Reverse $10%$ rule: $60 \div 0.1 = 600$.
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If a top predator has $2\ \text{kJ}$ after three $10%$ transfers, what producer energy was required?
If a top predator has $2\ \text{kJ}$ after three $10%$ transfers, what producer energy was required?
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$2000\ \text{kJ}$. Reverse three transfers: $2 \div (0.1)^3 = 2000$.
$2000\ \text{kJ}$. Reverse three transfers: $2 \div (0.1)^3 = 2000$.
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If producers have $30000\ \text{kJ}$, what percent remains at secondary consumers after two $10%$ transfers?
If producers have $30000\ \text{kJ}$, what percent remains at secondary consumers after two $10%$ transfers?
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$1%$. Two $10%$ transfers give $1%$ of original energy.
$1%$. Two $10%$ transfers give $1%$ of original energy.
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If $E_{p} = 4000\ \text{kJ}$ and efficiency is $12%$, what is $E_{n}$?
If $E_{p} = 4000\ \text{kJ}$ and efficiency is $12%$, what is $E_{n}$?
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$480\ \text{kJ}$. Calculate $12%$ of previous level: $4000 \times 0.12 = 480$.
$480\ \text{kJ}$. Calculate $12%$ of previous level: $4000 \times 0.12 = 480$.
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If $E_{p} = 7500\ \text{kJ}$ and efficiency is $8%$, what is $E_{n}$?
If $E_{p} = 7500\ \text{kJ}$ and efficiency is $8%$, what is $E_{n}$?
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$600\ \text{kJ}$. Calculate $8%$ of previous level: $7500 \times 0.08 = 600$.
$600\ \text{kJ}$. Calculate $8%$ of previous level: $7500 \times 0.08 = 600$.
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Calculate efficiency if $E_{p} = 2500\ \text{kJ}$ and $E_{n} = 50\ \text{kJ}$.
Calculate efficiency if $E_{p} = 2500\ \text{kJ}$ and $E_{n} = 50\ \text{kJ}$.
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$2%$. Use efficiency formula: $\frac{50}{2500} \times 100% = 2%$.
$2%$. Use efficiency formula: $\frac{50}{2500} \times 100% = 2%$.
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Find the number of trophic transfers if energy drops from $10000\ \text{kJ}$ to $10\ \text{kJ}$ at $10%$ each step.
Find the number of trophic transfers if energy drops from $10000\ \text{kJ}$ to $10\ \text{kJ}$ at $10%$ each step.
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3 transfers. Energy ratio is $(0.1)^3 = 0.001$, so 3 transfers.
3 transfers. Energy ratio is $(0.1)^3 = 0.001$, so 3 transfers.
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Find the number of trophic transfers if energy drops from $100000\ \text{kJ}$ to $100\ \text{kJ}$ at $10%$ each step.
Find the number of trophic transfers if energy drops from $100000\ \text{kJ}$ to $100\ \text{kJ}$ at $10%$ each step.
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3 transfers. Energy ratio is $(0.1)^3 = 0.001$, so 3 transfers.
3 transfers. Energy ratio is $(0.1)^3 = 0.001$, so 3 transfers.
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What is the general formula for energy after $n$ transfers with $10%$ efficiency from $E_0$?
What is the general formula for energy after $n$ transfers with $10%$ efficiency from $E_0$?
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$E_n = E_0 \times (0.1)^n$. General exponential decay formula with $10%$ efficiency.
$E_n = E_0 \times (0.1)^n$. General exponential decay formula with $10%$ efficiency.
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Using $E_n = E_0 \times (0.1)^n$, find $E_2$ if $E_0 = 6000\ \text{kJ}$.
Using $E_n = E_0 \times (0.1)^n$, find $E_2$ if $E_0 = 6000\ \text{kJ}$.
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$60\ \text{kJ}$. Two transfers: $6000 \times (0.1)^2 = 60$.
$60\ \text{kJ}$. Two transfers: $6000 \times (0.1)^2 = 60$.
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Using $E_n = E_0 \times (0.1)^n$, find $E_1$ if $E_0 = 4300\ \text{kJ}$.
Using $E_n = E_0 \times (0.1)^n$, find $E_1$ if $E_0 = 4300\ \text{kJ}$.
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$430\ \text{kJ}$. One transfer: $4300 \times 0.1 = 430$.
$430\ \text{kJ}$. One transfer: $4300 \times 0.1 = 430$.
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Using $E_n = E_0 \times (0.1)^n$, find $E_3$ if $E_0 = 9000\ \text{kJ}$.
Using $E_n = E_0 \times (0.1)^n$, find $E_3$ if $E_0 = 9000\ \text{kJ}$.
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$9\ \text{kJ}$. Three transfers: $9000 \times (0.1)^3 = 9$.
$9\ \text{kJ}$. Three transfers: $9000 \times (0.1)^3 = 9$.
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What is the quantitative reason energy pyramids are always upright (never inverted)?
What is the quantitative reason energy pyramids are always upright (never inverted)?
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Energy decreases each transfer due to heat loss; $E_{n} < E_{p}$. Energy loss from metabolism makes higher levels smaller.
Energy decreases each transfer due to heat loss; $E_{n} < E_{p}$. Energy loss from metabolism makes higher levels smaller.
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What is the formula for trophic transfer efficiency if $E_{n}$ is next level energy and $E_{p}$ is previous?
What is the formula for trophic transfer efficiency if $E_{n}$ is next level energy and $E_{p}$ is previous?
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$\text{Efficiency} = \frac{E_{n}}{E_{p}} \times 100%$. Standard formula for calculating energy transfer between levels.
$\text{Efficiency} = \frac{E_{n}}{E_{p}} \times 100%$. Standard formula for calculating energy transfer between levels.
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What is the definition of a trophic level in an ecosystem energy pyramid?
What is the definition of a trophic level in an ecosystem energy pyramid?
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A feeding position based on energy transfer (producer, consumer levels). Defines organisms' position in energy flow hierarchy.
A feeding position based on energy transfer (producer, consumer levels). Defines organisms' position in energy flow hierarchy.
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What is the primary energy source for most ecosystems that drives primary productivity?
What is the primary energy source for most ecosystems that drives primary productivity?
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Sunlight (solar energy). Photosynthesis converts solar energy into chemical energy for producers.
Sunlight (solar energy). Photosynthesis converts solar energy into chemical energy for producers.
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Identify the correct inequality for energy across trophic levels from producers to top predators.
Identify the correct inequality for energy across trophic levels from producers to top predators.
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$E_{\text{producers}} > E_{\text{primary}} > E_{\text{secondary}} > E_{\text{tertiary}}$. Energy decreases at each successive trophic level.
$E_{\text{producers}} > E_{\text{primary}} > E_{\text{secondary}} > E_{\text{tertiary}}$. Energy decreases at each successive trophic level.
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What does the $10%$ rule state about energy transfer between trophic levels?
What does the $10%$ rule state about energy transfer between trophic levels?
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About $10%$ of energy transfers; about $90%$ is lost as heat and metabolism. Standard rule describing energy transfer efficiency in ecosystems.
About $10%$ of energy transfers; about $90%$ is lost as heat and metabolism. Standard rule describing energy transfer efficiency in ecosystems.
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