all answers
A wildlife refuge contains 4,500 elk and covers 1,200 hectares of land. What is the population density in elk per square kilometer?
(1 km² = 100 hectares)
These may be separate or may be combined together into one equation. Units on intermediate steps aren't required, but final answer MUST have correct units stated
1200 hectares / 100 = 12 km2
4500 elk / 12 km2 = 375 elk / km2
A city’s population is growing at 1.75% annually. Approximately how many years will it take for the population to double? Round to the nearest whole year.
These may be separate or may be combined together into one equation. Units on intermediate steps aren't required, but final answer MUST have correct units stated
Use the rule of 70: 70 / 1.75 ≈ 40 years
Producers in a food web contain 80,000 kcal of energy. Approximately how much energy would be available to the secondary consumers?
Primary consumers: 80,000 * 0.10 = 8,000 kcal
Secondary consumers: 8,000 * 0.10 = 800 kcal
The net primary productivity of a grassland is 4,800 kcal/m²/year. Plant respiration is measured at 1,700 kcal/m²/year. What is the gross primary productivity?
4,800 + 1,700 = 6,500 kcal/m²/year
An ecosystem has a gross primary productivity of 9,500 kcal/m²/year and plant respiration of 3,200 kcal/m²/year. What is the net primary productivity?
9,500 − 3,200 = 6,300 kcal/m²/year
A hybrid vehicle travels 540 miles using 12 gallons of gasoline. What is the fuel efficiency of the vehicle in miles per gallon?
A fish population decreased from 12,000 individuals to 9,000 individuals. What was the percent change?
((9,000 − 12,000) / 12,000) * 100 =
(−3,000 / 12,000) * 100 =
−25% (or 25% reduction)
the formula for population density is:
population / area = POPULATION DENSITY
A wetland originally covered 850 acres. After years of development, only 595 acres remain. What was the percent decrease in wetland area?
(595 acres - 850 acres) / 850 acres *100 = -30% or a 30% decrease
the rule of 70 is:
70 / (percent growth rate) = TIME TO DOUBLE POPULATION
the formula for population growth rate as a percent is:
(births - deaths) / (population size) *100 = POPULATION GROWTH RATE (percent)
Atmospheric methane concentration increased from 1,720 ppb to 1,940 ppb between 2005 and 2016. What was the average annual rate of change in ppb per year?
1940 - 1720 ppb = 220 ppb 2016 - 2005 = 11 years
220 ppb / 11 years = 20 ppb / year
A grassland ecosystem contains 950,000 kcal of energy in producer biomass. Approximately how much energy would be available to tertiary consumers?
Primary consumers: 95,000 kcal
Secondary consumers: 9,500 kcal
Tertiary consumers: 950 kcal
(multiply biomass by 10% for each successive tropic level)
rate of change formula:
RATE OF CHANGE = (final value - initial value) / (final time - initial time) * 100
percent change formula:
(final value - initial value) / (initial value) * 100 = PERCENT CHANGE
Two pesticides are tested on rats.
Which pesticide is more toxic, and why?
Pesticide A is more toxic because a smaller dose is required to kill 50% of the test organisms.
A country’s population is expected to double in approximately 28 years. According to the Rule of 70, what is the country’s annual population growth rate?
70 / 28 = 2.5 %
A chemical has an LD50 of 40 mg/kg. Approximately how many milligrams of the chemical would represent the LD50 dose for a 65 kg person?
40 mg/kg * 65 kg = 2,600 mg
In a toxicity study, scientists expose groups of 100 mice to different doses of a chemical. Estimate the LD50 of the chemical.
LD50 is the dose that kills approximately 50% of organisms. Around 50% mortality occurs between 30 and 40 mg/kg, but 40 mg/kg gives 51 deaths out of 100.
Estimated LD50 ≈ 40 mg/kg
An ecosystem has a gross primary productivity of 18,400 kcal/m²/year. Producers use 38% of this energy during respiration. What is the net primary productivity?
Respiration = 18,400 × 0.38 = 6,992 kcal/m²/year
NPP = 18,400 − 6,992 = 11,408 kcal/m²/year
OR 18400 - (18400 * 0.38) = 11,408 kcal/m²/year
A vehicle travels 180 miles on the highway at 36 mpg and then drives 120 miles in the city at 24 mpg. What is the vehicle’s overall fuel efficiency for the entire trip?
Highway fuel used: 180 ÷ 36 = 5 gallons
City fuel used: 120 ÷ 24 = 5 gallons
Total distance = 300 miles
Total fuel = 10 gallons
300 miles / 10 gallons = 30 miles per gallon (or 30 mpg or 30 miles / gallon)
the formula for net primary productivity (NPP):
Gross primary productivity (GPP) - Respiration = NPP
A country has a crude birth rate of 31 births per 1,000 people and a crude death rate of 14 deaths per 1,000 people. If the country also experiences a net migration rate of −0.3%, what is the overall population growth rate?
Natural increase: (31 − 14) ÷ 1000 = 0.017 *100 = 1.7%
take away the population lost to migration: 1.7% - 0.3% = 1.4%
the formula for Gross Primary Productivity (GPP) is:
GPP = (Total solar energy captured by plants) − (Energy lost due to respiration by plants)
GPP is the rate of photosynthesis done by plants
A coal-fired power plant emits 4.2 metric tons of sulfur dioxide each day. How many kilograms of sulfur dioxide are emitted in 3 weeks?
(1 metric ton = 1,000 kg)
3 weeks = 21 days
4.2 metric tons/day * 21 days = 88.2 metric tons
88.2 * 1,000 = 88,200 kg