1. The magnitude M of an earthquake on the Richter scale may be defined by the formula M = 0.67 log(0.37E) + 1.46 where E is the energy of the earthquake in Kilowatt hours. What is the energy of an earthquake of magnitude 8.1 ? (Mt. St. Helens)
2. When the skeleton of a wooly mammoth is discovered in the Siberian tundra, it is found that the level of radioactivity in the skeleton is 14% of that of a living animal. Estimate how long ago the mammoth lived.(Half-life of carbon-14 = 5700 yrs.)
3. The population of the earth in 1925 was about 2 billion. If the population doubles every 75 years, in what approximate year will there be one person for each of the 1.5 x 1014 square meters of land on the earth?
4. The magnitude of a star is defined by the formula M = -2.5 log(kl) where k is a constant and I is the intensity of the light from the star. What is the ratio of the intensities of light from the star Sirius, which has a magnitude of -1.6, and from the star Betelgeuse, which has a magnitude of 0.9?
5. Uranium-238 (U238) decomposes into lead-206 (Pb206) with a half-life of 4.5 billion years. In a volcanic eruption, the lead is removed from the lava. If a sample of lava has 1 part Pb206 to 99 parts U238, how many years ago was the volcanic eruption that formed it?
6. Assume that if the temperature is constant, then the atmospheric pressure p varies with the altitude h (above sea level) in such a way that p=poekh where k is a constant and po is the atmospheric pressure at sea level. Find the pressure at 10,000 feet if p measures 15 Ib/in2 at sea level, and 12 Ib/in2 at 5000 feet above sea level.
7. The town of Grayrock had a population of 10,000 in 1960 and 12,Q00 in 1970.
a) Assuming an exponential growth model, estimate the population in 1990.
b) What is the doubling time for the town's population?
8. Forty percent of a radioactive substance decays in 5 years. Find the half-life of a substance.
9. The initial estimate of the 1989 oil slick in the Prince William Sound was given to cover approximately 10 square miles and doubling every 36 hours.
a. In a week's time, what could be the expected coverage in square miles?
b. When would the oil slick reach 600 square miles?
10. Before all was said and done, the Exxon Valdez would leak 10 million gallons of crude oil into the sound. Assuming these gallons of oil were decreasing exponentially from the tanker at a rate of 2% every 4 hours;
a. how many gallons had leaked in one day?
b. how long before the Valdez had leaked one-half of it's load?
11. The devastating earthquake that rocked San Francisco during the World Series a few years ago, registered a magnitude of approximately 7.2 on the Richter Scale. Given that the magnitude, M of an earthquake is defined by
M = 0.67 log (0.37E) + 1.46
where E is the energy in kwh, find:
a. How much energy was released by the San Fransisco quake?
b. According to LES engineers, Lincoln uses approximately 460 megawatts of energy per month on an average during the peak summer months. If one could feasibly harness the energy, say from the San Fransisco quake, for how long could a city the size of Lincoln expect to run at peak energy demand?