MAT 205 Homework 2

1. A king in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the king would place two grains of wheat, on the third square, four gains of wheat, and on the fourth square eight grains of wheat. if the amount of wheat is doubled in this way on each of the remaining squares how many grians of wheat should be placed on square 14? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds. (assume that each grain of wheat weights 1/700 pounds)2. A king in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the king would place two grains of wheat, on the third square, four gains of wheat, and on the fourth square eight grains of wheat. if the amount of wheat is doubled in this way on each of the remaining squares how many grians of wheat should be placed on square 18? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds. (assume that each grain of wheat weights 1/700 pounds)3. A king in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the king would place two grains of wheat, on the third square, four gains of wheat, and on the fourth square eight grains of wheat. if the amount of wheat is doubled in this way on each of the remaining squares how many grians of wheat should be placed on square 237? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds. (assume that each grain of wheat weights 1/700 pounds)4. the doubling time of a population of flies is 5 hours. by what factor does the population increase in 30 hours? By what factor does the population increase in 2 weeks?5. Scientists believe that earth once had 10 trillion tons of a naturally existing plutonium isotope (back when the earth was formed). Given a half life of 25,000 years for that specific plutonium isotope and the earth’s current age of 4.6 billion years, how much would remain today? Use your answer to explain why this isotope is not found naturally on earth today. The remaining amount after 4.6 billion years will be __ tons.6. Use an annual growth rate of 1.6% in a 30 year period for a certain population to find the approximate doubling time and then predict the population in 2050, based on a 2000 population of 60 billion. What is the approximate doubling time? ___ years7. How much energy , in joules, is released by an earthquake of magnitude 6?8. How many time greater is the intensity of sound from a concert speaker at a distance of 1 meter than the intensity at a distance of 14 meters. The intensity of sound is ___ times as strong at 1 m as at 14 m?9. Suppose the pH of a solution decreases by 5. How does the hydrogen ion concentrate change? The new hydrogen ion concentration is __ times the initial concentration

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