Biology Flashcards: Apply Math To Energy Flow

What this deck covers

This deck focuses on Apply Math To Energy Flow, giving you a quick way to review the definitions, rules, and examples that matter most for Biology.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Which process is the main reason energy is not fully transferred to the next trophic level?

Answer: Respiration and heat loss during metabolism. Cellular respiration converts energy to heat, reducing transfer.

Flashcard 2: Find energy lost if $E_{p} = 2500\ \text{kJ}$ and $E_{n} = 125\ \text{kJ}$.

Answer: $2375\ \text{kJ}$. Subtract transferred from previous: $2500 - 125 = 2375$.

Flashcard 3: How much energy remains after two $10\%$ transfers starting from $10000\ \text{kJ}$?

Answer: $100\ \text{kJ}$. Two $10\%$ transfers: $10000 \times (0.1)^2 = 100$.

Flashcard 4: If tertiary consumers have $8\ \text{kJ}$ and transfer is $10\%$, what was secondary consumer energy?

Answer: $80\ \text{kJ}$. Reverse $10\%$ rule: $8 \div 0.1 = 80$.

Flashcard 5: Find the energy at the next trophic level if a level has $5000\ \text{kJ}$ and transfer is $10\%$.

Answer: $500\ \text{kJ}$. Apply $10\%$ rule: $5000 \times 0.1 = 500$.

Flashcard 6: If $E_{p} = 4000\ \text{kJ}$ and efficiency is $12\%$, what is $E_{n}$?

Answer: $480\ \text{kJ}$. Calculate $12\%$ of previous level: $4000 \times 0.12 = 480$.

Flashcard 7: If a top predator has $2\ \text{kJ}$ after three $10\%$ transfers, what producer energy was required?

Answer: $2000\ \text{kJ}$. Reverse three transfers: $2 \div (0.1)^3 = 2000$.

Flashcard 8: Find the number of trophic transfers if energy drops from $100000\ \text{kJ}$ to $100\ \text{kJ}$ at $10\%$ each step.

Answer: 3 transfers. Energy ratio is $(0.1)^3 = 0.001$, so 3 transfers.

Flashcard 9: If $E_{p} = 4000\ \text{kJ}$ and efficiency is $12\%$, what is $E_{n}$?

Answer: $480\ \text{kJ}$. Calculate $12\%$ of previous level: $4000 \times 0.12 = 480$.

Flashcard 10: What is the definition of a food chain in quantitative energy transfer terms?

Answer: A linear pathway of energy transfer through feeding relationships. Simple pathway showing direct energy transfer sequence.

Flashcard 11: What is the primary energy source for most ecosystems that drives primary productivity?

Answer: Sunlight (solar energy). Photosynthesis converts solar energy into chemical energy for producers.

Flashcard 12: What is the definition of a secondary consumer in terms of energy source?

Answer: A consumer that obtains energy by eating primary consumers. Second-level consumers feeding on primary consumers.

Flashcard 13: Calculate $\text{GPP}$ if $\text{NPP} = 700$ and producer respiration $R = 300$ (same units).

Answer: $1000$. Rearrange NPP formula: $700 + 300 = 1000$.

Flashcard 14: What is the definition of biomass in ecosystem energy flow problems?

Answer: Total mass of living organic matter in a trophic level. Quantifies living organic matter available for energy transfer.

Flashcard 15: Find the energy at the next trophic level if a level has $5000\ \text{kJ}$ and transfer is $10\%$.

Answer: $500\ \text{kJ}$. Apply $10\%$ rule: $5000 \times 0.1 = 500$.

Flashcard 16: What is the typical unit for energy flow in an energy pyramid (rate per area)?

Answer: $\text{kJ}\,\text{m}^{-2}\,\text{yr}^{-1}$ (or similar energy/area/time). Standard units express energy flux per area per time.

Flashcard 17: How much energy remains after four $10\%$ transfers starting from $200000\ \text{kJ}$?

Answer: $20\ \text{kJ}$. Four $10\%$ transfers: $200000 \times (0.1)^4 = 20$.

Flashcard 18: How much energy remains after two $10\%$ transfers starting from $10000\ \text{kJ}$?

Answer: $100\ \text{kJ}$. Two $10\%$ transfers: $10000 \times (0.1)^2 = 100$.

Flashcard 19: Find the number of trophic transfers if energy drops from $10000\ \text{kJ}$ to $10\ \text{kJ}$ at $10\%$ each step.

Answer: 3 transfers. Energy ratio is $(0.1)^3 = 0.001$, so 3 transfers.

Flashcard 20: What is a common quantitative estimate for the fraction of energy lost between trophic levels?

Answer: About $90\%$ lost between levels. Standard estimate based on metabolic energy losses.

Flashcard 21: Using $E_n = E_0 \times (0.1)^n$, find $E_2$ if $E_0 = 6000\ \text{kJ}$.

Answer: $60\ \text{kJ}$. Two transfers: $6000 \times (0.1)^2 = 60$.

Flashcard 22: What is the relationship between $\text{NPP}$, $\text{GPP}$, and producer respiration $R$?

Answer: $\text{NPP} = \text{GPP} - R$. Standard equation relating gross and net primary productivity.

Flashcard 23: What does the $10\%$ rule state about energy transfer between trophic levels?

Answer: About $10\%$ of energy transfers; about $90\%$ is lost as heat and metabolism. Standard rule describing energy transfer efficiency in ecosystems.

Flashcard 24: If assimilated energy is $300\ \text{kJ}$ and respiration is $250\ \text{kJ}$, what is production $P$ (new biomass)?

Answer: $50\ \text{kJ}$. Subtract respiration from assimilated: $300 - 250 = 50$.

Flashcard 25: Which trophic level is always the base of an energy pyramid?

Answer: Primary producers (autotrophs). Producers capture energy from sunlight via photosynthesis.

Flashcard 26: If $E_{p} = 7500\ \text{kJ}$ and efficiency is $8\%$, what is $E_{n}$?

Answer: $600\ \text{kJ}$. Calculate $8\%$ of previous level: $7500 \times 0.08 = 600$.

Flashcard 27: Identify the correct inequality for energy across trophic levels from producers to top predators.

Answer: $E_{\text{producers}} > E_{\text{primary}} > E_{\text{secondary}} > E_{\text{tertiary}}$. Energy decreases at each successive trophic level.

Flashcard 28: What is the formula for assimilated energy $A$ if ingestion is $I$ and egestion is $F$?

Answer: $A = I - F$. Standard formula for consumer energy assimilation.

Flashcard 29: What is the formula for trophic transfer efficiency if $E_{n}$ is next level energy and $E_{p}$ is previous?

Answer: $\text{Efficiency} = \frac{E_{n}}{E_{p}} \times 100\%$. Standard formula for calculating energy transfer between levels.

Flashcard 30: If $90\%$ of energy is lost each transfer, what fraction is transferred to the next trophic level?

Answer: $10\%$ (fraction $0.1$). If $90\%$ lost, then $10\%$ transferred to next level.

Flashcard 31: What is the definition of a decomposer in ecosystem energy flow?

Answer: An organism that breaks down dead organic matter and wastes for energy. Recycles nutrients by breaking down dead organic matter.

Flashcard 32: If tertiary consumers have $8\ \text{kJ}$ and transfer is $10\%$, what was secondary consumer energy?

Answer: $80\ \text{kJ}$. Reverse $10\%$ rule: $8 \div 0.1 = 80$.

Flashcard 33: Calculate $\text{GPP}$ if $\text{NPP} = 700$ and producer respiration $R = 300$ (same units).

Answer: $1000$. Rearrange NPP formula: $700 + 300 = 1000$.

Flashcard 34: If primary consumers have $900\ \text{kJ}$, estimate energy available to secondary consumers using $10\%$.

Answer: $90\ \text{kJ}$. Apply $10\%$ rule: $900 \times 0.1 = 90$.

Flashcard 35: Calculate efficiency if $E_{p} = 2500\ \text{kJ}$ and $E_{n} = 50\ \text{kJ}$.

Answer: $2\%$. Use efficiency formula: $\frac{50}{2500} \times 100\% = 2\%$.

Flashcard 36: Which trophic level has the least available energy in a typical energy pyramid?

Answer: Top predators (highest-level consumers). Multiple energy transfers result in least energy at top.

Flashcard 37: Find energy lost if $E_{p} = 9000\ \text{kJ}$ and $E_{n} = 900\ \text{kJ}$.

Answer: $8100\ \text{kJ}$. Subtract transferred from previous: $9000 - 900 = 8100$.

Flashcard 38: What does an energy pyramid represent, quantitatively, at each trophic level?

Answer: Energy available per unit area per unit time at each level. Shows energy availability decreasing at higher trophic levels.

Flashcard 39: What is the general formula for energy after $n$ transfers with $10\%$ efficiency from $E_0$?

Answer: $E_n = E_0 \times (0.1)^n$. General exponential decay formula with $10\%$ efficiency.

Flashcard 40: Calculate efficiency if $E_{p} = 2500\ \text{kJ}$ and $E_{n} = 50\ \text{kJ}$.

Answer: $2\%$. Use efficiency formula: $\frac{50}{2500} \times 100\% = 2\%$.

Flashcard 41: If producers store $12000\ \text{kJ}$ as NPP, estimate energy available to primary consumers using $10\%$.

Answer: $1200\ \text{kJ}$. Apply $10\%$ rule to NPP: $12000 \times 0.1 = 1200$.

Flashcard 42: If producers have $30000\ \text{kJ}$, what percent remains at secondary consumers after two $10\%$ transfers?

Answer: $1\%$. Two $10\%$ transfers give $1\%$ of original energy.

Flashcard 43: If secondary consumers have $60\ \text{kJ}$ and transfer is $10\%$, what was primary consumer energy?

Answer: $600\ \text{kJ}$. Reverse $10\%$ rule: $60 \div 0.1 = 600$.

Flashcard 44: If a consumer ingests $500\ \text{kJ}$ and egests $200\ \text{kJ}$, what is assimilated energy $A$?

Answer: $300\ \text{kJ}$. Subtract egested from ingested: $500 - 200 = 300$.

Flashcard 45: Calculate trophic efficiency if $E_{p} = 8000\ \text{kJ}$ and $E_{n} = 400\ \text{kJ}$.

Answer: $5\%$. Use efficiency formula: $\frac{400}{8000} \times 100\% = 5\%$.

Flashcard 46: What is the formula for consumer production $P$ if assimilation is $A$ and respiration is $R$?

Answer: $P = A - R$. Standard formula for net biomass production by consumers.

Flashcard 47: Which trophic level has the least available energy in a typical energy pyramid?

Answer: Top predators (highest-level consumers). Multiple energy transfers result in least energy at top.

Flashcard 48: Find energy lost if $E_{p} = 2500\ \text{kJ}$ and $E_{n} = 125\ \text{kJ}$.

Answer: $2375\ \text{kJ}$. Subtract transferred from previous: $2500 - 125 = 2375$.

Flashcard 49: What is the definition of net primary productivity (NPP)?

Answer: Energy stored as biomass after producer respiration. Energy available to consumers after producer respiration losses.

Flashcard 50: What is the definition of gross primary productivity (GPP)?

Answer: Total energy captured by photosynthesis per unit time. Total energy fixed by producers before accounting for their respiration.

Flashcard 51: If a consumer ingests $500\ \text{kJ}$ and egests $200\ \text{kJ}$, what is assimilated energy $A$?

Answer: $300\ \text{kJ}$. Subtract egested from ingested: $500 - 200 = 300$.

Flashcard 52: If $E_{p} = 7500\ \text{kJ}$ and efficiency is $8\%$, what is $E_{n}$?

Answer: $600\ \text{kJ}$. Calculate $8\%$ of previous level: $7500 \times 0.08 = 600$.

Flashcard 53: Find energy lost if $E_{p} = 9000\ \text{kJ}$ and $E_{n} = 900\ \text{kJ}$.

Answer: $8100\ \text{kJ}$. Subtract transferred from previous: $9000 - 900 = 8100$.

Flashcard 54: If a top predator has $2\ \text{kJ}$ after three $10\%$ transfers, what producer energy was required?

Answer: $2000\ \text{kJ}$. Reverse three transfers: $2 \div (0.1)^3 = 2000$.

Flashcard 55: Find the number of trophic transfers if energy drops from $100000\ \text{kJ}$ to $100\ \text{kJ}$ at $10\%$ each step.

Answer: 3 transfers. Energy ratio is $(0.1)^3 = 0.001$, so 3 transfers.

Flashcard 56: How much energy remains after three $10\%$ transfers starting from $50000\ \text{kJ}$?

Answer: $50\ \text{kJ}$. Three $10\%$ transfers: $50000 \times (0.1)^3 = 50$.

Flashcard 57: If producers store $12000\ \text{kJ}$ as NPP, estimate energy available to primary consumers using $10\%$.

Answer: $1200\ \text{kJ}$. Apply $10\%$ rule to NPP: $12000 \times 0.1 = 1200$.

Flashcard 58: If secondary consumers have $60\ \text{kJ}$ and transfer is $10\%$, what was primary consumer energy?

Answer: $600\ \text{kJ}$. Reverse $10\%$ rule: $60 \div 0.1 = 600$.

Flashcard 59: What is the relationship between $\text{NPP}$, $\text{GPP}$, and producer respiration $R$?

Answer: $\text{NPP} = \text{GPP} - R$. Standard equation relating gross and net primary productivity.

Flashcard 60: What is the formula to find energy lost between trophic levels if $E_{p}$ is previous and $E_{n}$ is next?

Answer: $E_{\text{lost}} = E_{p} - E_{n}$. Difference between energy inputs and outputs between levels.

Flashcard 61: Using $E_n = E_0 \times (0.1)^n$, find $E_3$ if $E_0 = 9000\ \text{kJ}$.

Answer: $9\ \text{kJ}$. Three transfers: $9000 \times (0.1)^3 = 9$.

Flashcard 62: Which process is the main reason energy is not fully transferred to the next trophic level?

Answer: Respiration and heat loss during metabolism. Cellular respiration converts energy to heat, reducing transfer.

Flashcard 63: How much energy remains after three $10\%$ transfers starting from $50000\ \text{kJ}$?

Answer: $50\ \text{kJ}$. Three $10\%$ transfers: $50000 \times (0.1)^3 = 50$.

Flashcard 64: What is the definition of net primary productivity (NPP)?

Answer: Energy stored as biomass after producer respiration. Energy available to consumers after producer respiration losses.

Flashcard 65: What is the definition of a primary consumer in terms of energy source?

Answer: A consumer that obtains energy by eating producers. First-level consumers feeding directly on producers.

Flashcard 66: What is the definition of biomass in ecosystem energy flow problems?

Answer: Total mass of living organic matter in a trophic level. Quantifies living organic matter available for energy transfer.

Flashcard 67: If $90\%$ of energy is lost each transfer, what fraction is transferred to the next trophic level?

Answer: $10\%$ (fraction $0.1$). If $90\%$ lost, then $10\%$ transferred to next level.

Flashcard 68: Using $E_n = E_0 \times (0.1)^n$, find $E_3$ if $E_0 = 9000\ \text{kJ}$.

Answer: $9\ \text{kJ}$. Three transfers: $9000 \times (0.1)^3 = 9$.

Flashcard 69: What is the definition of a food web compared with a food chain?

Answer: A network of interconnected food chains showing multiple energy pathways. Complex system with multiple interconnected feeding relationships.

Flashcard 70: Calculate producer respiration $R$ if $\text{GPP} = 2200$ and $\text{NPP} = 1600$ (same units).

Answer: $600$. Rearrange NPP formula: $2200 - 1600 = 600$.

Flashcard 71: Calculate $\text{NPP}$ if $\text{GPP} = 1500$ and producer respiration $R = 600$ (same units).

Answer: $900$. Use NPP formula: $1500 - 600 = 900$.

Flashcard 72: Which trophic level is always the base of an energy pyramid?

Answer: Primary producers (autotrophs). Producers capture energy from sunlight via photosynthesis.

Flashcard 73: What is the definition of ecological efficiency in energy flow?

Answer: Percent of energy at one trophic level transferred to the next. Measures efficiency of energy transfer between trophic levels.

Flashcard 74: Calculate efficiency if $E_{p} = 3600\ \text{kJ}$ and $E_{n} = 540\ \text{kJ}$.

Answer: $15\%$. Use efficiency formula: $\frac{540}{3600} \times 100\% = 15\%$.

Flashcard 75: Calculate trophic efficiency if $E_{p} = 12000\ \text{kJ}$ and $E_{n} = 1800\ \text{kJ}$.

Answer: $15\%$. Use efficiency formula: $\frac{1800}{12000} \times 100\% = 15\%$.

Flashcard 76: What does an energy pyramid represent, quantitatively, at each trophic level?

Answer: Energy available per unit area per unit time at each level. Shows energy availability decreasing at higher trophic levels.

Flashcard 77: What is the definition of a primary consumer in terms of energy source?

Answer: A consumer that obtains energy by eating producers. First-level consumers feeding directly on producers.

Flashcard 78: What is the definition of a trophic level in an ecosystem energy pyramid?

Answer: A feeding position based on energy transfer (producer, consumer levels). Defines organisms' position in energy flow hierarchy.

Flashcard 79: What is the definition of a decomposer in ecosystem energy flow?

Answer: An organism that breaks down dead organic matter and wastes for energy. Recycles nutrients by breaking down dead organic matter.

Flashcard 80: What is the definition of ecological efficiency in energy flow?

Answer: Percent of energy at one trophic level transferred to the next. Measures efficiency of energy transfer between trophic levels.

Flashcard 81: Calculate efficiency if $E_{p} = 3600\ \text{kJ}$ and $E_{n} = 540\ \text{kJ}$.

Answer: $15\%$. Use efficiency formula: $\frac{540}{3600} \times 100\% = 15\%$.

Flashcard 82: Find the energy at the next trophic level if producers have $20000\ \text{kJ}$ and efficiency is $10\%$.

Answer: $2000\ \text{kJ}$. Apply $10\%$ rule: $20000 \times 0.1 = 2000$.

Flashcard 83: Using $E_n = E_0 \times (0.1)^n$, find $E_2$ if $E_0 = 6000\ \text{kJ}$.

Answer: $60\ \text{kJ}$. Two transfers: $6000 \times (0.1)^2 = 60$.

Flashcard 84: Find the energy at the next trophic level if producers have $20000\ \text{kJ}$ and efficiency is $10\%$.

Answer: $2000\ \text{kJ}$. Apply $10\%$ rule: $20000 \times 0.1 = 2000$.

Flashcard 85: What is the definition of a food web compared with a food chain?

Answer: A network of interconnected food chains showing multiple energy pathways. Complex system with multiple interconnected feeding relationships.

Flashcard 86: What is the primary energy source for most ecosystems that drives primary productivity?

Answer: Sunlight (solar energy). Photosynthesis converts solar energy into chemical energy for producers.

Flashcard 87: What is the definition of a food chain in quantitative energy transfer terms?

Answer: A linear pathway of energy transfer through feeding relationships. Simple pathway showing direct energy transfer sequence.

Flashcard 88: What is the definition of net secondary productivity (NSP) for consumers in energy terms?

Answer: Consumer energy stored as new biomass after respiration and waste losses. Consumer equivalent of NPP for energy storage efficiency.

Flashcard 89: What is the formula to find energy lost between trophic levels if $E_{p}$ is previous and $E_{n}$ is next?

Answer: $E_{\text{lost}} = E_{p} - E_{n}$. Difference between energy inputs and outputs between levels.

Flashcard 90: What does it mean if trophic efficiency is $20\%$ instead of $10\%$?

Answer: A larger fraction of energy is transferred to the next trophic level. Higher efficiency means less energy lost per transfer.

Flashcard 91: Calculate producer respiration $R$ if $\text{GPP} = 2200$ and $\text{NPP} = 1600$ (same units).

Answer: $600$. Rearrange NPP formula: $2200 - 1600 = 600$.

Flashcard 92: If primary consumers have $900\ \text{kJ}$, estimate energy available to secondary consumers using $10\%$.

Answer: $90\ \text{kJ}$. Apply $10\%$ rule: $900 \times 0.1 = 90$.

Flashcard 93: What is the quantitative reason energy pyramids are always upright (never inverted)?

Answer: Energy decreases each transfer due to heat loss; $E_{n} < E_{p}$. Energy loss from metabolism makes higher levels smaller.

Flashcard 94: Calculate $\text{NPP}$ if $\text{GPP} = 1500$ and producer respiration $R = 600$ (same units).

Answer: $900$. Use NPP formula: $1500 - 600 = 900$.

Flashcard 95: What does the $10\%$ rule state about energy transfer between trophic levels?

Answer: About $10\%$ of energy transfers; about $90\%$ is lost as heat and metabolism. Standard rule describing energy transfer efficiency in ecosystems.

Flashcard 96: What is the quantitative reason energy pyramids are always upright (never inverted)?

Answer: Energy decreases each transfer due to heat loss; $E_{n} < E_{p}$. Energy loss from metabolism makes higher levels smaller.

Flashcard 97: What is a common quantitative estimate for the fraction of energy lost between trophic levels?

Answer: About $90\%$ lost between levels. Standard estimate based on metabolic energy losses.

Flashcard 98: What is the definition of a trophic level in an ecosystem energy pyramid?

Answer: A feeding position based on energy transfer (producer, consumer levels). Defines organisms' position in energy flow hierarchy.

Flashcard 99: What is the typical unit for energy flow in an energy pyramid (rate per area)?

Answer: $\text{kJ}\,\text{m}^{-2}\,\text{yr}^{-1}$ (or similar energy/area/time). Standard units express energy flux per area per time.

Flashcard 100: What is the definition of gross primary productivity (GPP)?

Answer: Total energy captured by photosynthesis per unit time. Total energy fixed by producers before accounting for their respiration.