APES Math Formulas and Population Growth Review 2025

Percent Change

% increase = (New Value - Initial Value) / Initial Value X 100

Rule of 70

of years to double = 70 / Annual % growth rate

Population Growth Rate

r = (b + i) - (d + e) x 100 / total population

Crude Growth Rate

Crude Growth Rate (r) = (CBR - CDR) / 10

Multiplication Factor

1,000,000,000 = 10^9

Prefix Symbol for Giga

giga G

Multiplication Factor for Mega

1,000,000 = 10^6

Multiplication Factor for Kilo

1,000 = 10^3

Multiplication Factor for Hecto

100 = 10^2

Multiplication Factor for Deci

0.1 = 10^-1

Multiplication Factor for Centi

0.01 = 10^-2

Multiplication Factor for Milli

0.001 = 10^-3

Multiplication Factor for Micro

0.000001 = 10^-6

Multiplication Factor for Nano

0.000000001 = 10^-9

Half Life Formula

amount remaining = (original amount) x (0.5)^x, where x = number of half lives

Rate of Change Formula

Rate of change = (final value - initial value) / (final year - initial year)

Total Energy Used Formula

Total energy used = kW x hours = kWh

Energy Efficiency Formula

Energy Efficiency = efficiency of step 1 x efficiency of step 2, etc. x 100

Primary Productivity Formula

NPP = GPP - R

10% Rule

10% of all energy moves from one trophic level to the next

Per Capita Measurement

Per capita = population measurement / population size