Important Formulas to Memorize for APES

Lincoln Index

A statistical measure used to estimate population sizes, calculated as (E1)(E2)/S.

Population Growth Rate (PGR)

Calculated by (Number of Births - Number of Deaths)/(Total Population Size), indicating how quickly a population is expanding or contracting.

Energy Conversion

1 kJ = 1000 Joules; 1 kcal = 1000 calories; 1 calorie = 4.184 joules.

Power formula

Calculated as Power = Energy/Time.

Population Growth Rate (percentage)

Calculated as (Births - Deaths) / Total Population x 100, indicating percentage change in a population.

Percent Change formula

(New Value - Old Value) / Old Value x 100, calculating the percentage difference between two values.

Rule of 70 formula

70 / Growth Rate, used to estimate the time for a population to double.

Population Density formula

Total Population / Land Area, measuring the number of individuals in a specific area.

Efficiency formula

Energy Output / Energy Input x 100, indicating the percentage of energy conversion.

Rate of Change formula

Final - Initial / Final time - Initial time, measuring the change over time.

Gross Primary Productivity (GPP)

GPP = Total solar energy captured by plants − Energy lost due to respiration.

Net Primary Productivity (NPP)

NPP = Gross primary productivity (GPP) - Respiration.

The 10% Rule

Only approximately 10% of energy transfers between trophic levels in a food chain.

Dimensional Analysis

Quantity 1 x (Conversion factor / Quantity 2 ) = Result, used to convert units.

Half-Life formula

t½ = ln (2) / λ, where t1/2 is the half-life and λ is the decay constant.

Respiration equation

C6H12O6 + 6O2 → 6CO2 + 6H2O, the process by which organisms convert glucose into energy.

Combustion reaction

Hydrocarbons (CxHy) + O2 → CO2 + H2O, representing the burning of hydrocarbons.

Photosynthesis equation

6CO2 + 6H2O + sunlight → C6H12O6 + 6O2, the process through which plants convert light energy into chemical energy.

Ocean Acidification equation

CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3-, demonstrating the chemical reactions involved in ocean acidification.

Photochemical Smog Formation

NOx + VOCs + heat + sunlight → smog, describing the reaction that leads to smog formation.

Stratospheric Ozone Depletion equation

O3 + Cl → O2 + ClO, representing the chemical reaction responsible for ozone layer depletion.