Nonrenewables Quiz Answer Key for Math Problems
(A4, B1) I-131 has a half-life of about 8 days. If an original sample weighs 240 kg, how many kg will remain after 24 days?
In 24 days there are 3 half-lives: after 8 days 120 kg will remain, after 16 days 60 kg will remain, and
after 24 days 30 kg will remain
(A1, B2) A home uses ten 100-watt lightbulbs for five hours per day. Approximately how many kilowatt-hours of electrical energy are consumed in one year by using the light bulbs?
For each light bulb:100w * 1kw/1000w * 5hours/day * 365days/year = 182.5 kwh/year
There are 10 light bulbs: 182.5 kwh/year * 10= 1,825 kwh/year
3. In 1997 the World Resources Institute estimated the world's proven oil reserves to be 1,000 billion barrels and the ultimately recoverable reserves to be 2,000 billion barrels. The table below shows the world consumption of oil from 1986 to 1997.
Year Consumption (million barrels per day)
1986 62
1987 63
1988 65
1989 66
1990 66
1991 67
1992 67
1993 67
1994 68
1995 70
1996 72
1997 74
a) At the 1997 rate of consumption, about how long (years) will the estimated 2,000 billion barrels of oil last?
2.0 x 1012 barrels remaining / (7.4 x 107 barrels/day)= 2.7 x 104 days remaining
2.7 x 104 days * 1 year = 74 years
365 days
b) What was the approximate percent increase in consumption from 1986 to 1997?
(7.4 x 107 barrels/day) - (6.2 x 107 barrels/day)≈ 19%
6.2 x 107 barrels/day
(A2, B4) The half-life of radon gas is approximately four days. Four weeks after the introduction of radon into a sealed room, what fraction of the original amount is remaining?
There are 7 half-lives in 28 days: 1 1/2 1/4 1/8 1/16 1/32 1/64 1/128
5. The Cobb family of Fremont is looking at ways to decrease their home water and energy usage. Their current hot-water heater raises the water temperature to 140F, which requires 0.20 kWh/gallon of water at a cost of $0.10/kWh. Each person in the family of four showers once a day for an average of 10 minutes per shower. The shower has a flow rate of 5.0 gallons per minute. Calculate the following. Be sure to show all your work and include units with your answers.
a) The total amount of water that the family uses per year for taking showers.
10min/day per person * 5gal/min * 365day/year * 4 persons = 73,000 gal/year
b) The annual cost of the electricity for the family showers, assuming that 2.5 gallons per minute
of the water used is from the hot-water heater.
73,000 gal/year for showers, but only 2.5 gal/shower (1/2 the water) comes from the hot water heater=
36,500 gal of hot water/ year
36,500gal/year * 0.2kwh/gal * $0.10/kwh = $730/year