Name Math 1050 Project #5 Fall 2017 Part #1: Doubling Time versus the Initial Amount (6 points) 1. Would you rather start with one penny ($0.01) and double your wealth every day or start with one dime ($0.10) and double your wealth every five days, assuming that you want to enrich yourself? Justify your answer mathematically and explain your reasoning. I would rather have the penny. After only ten days the penny would have accumulated to $10.24 while the dime would only be worth 20 cents. Using math to justify for the penny .01*(2^5)=.32 and for the dime .10*(2^1)=.20 so after only five days the penny is already worth more. 2. Would you rather start with one penny ($0.01) and double your wealth every day or start with $1000 and double your wealth every two days, assuming that you want to enrich yourself? Justify your answer mathematically and explain your reasoning. I would rather have 3. Which is more important in determining how fast exponential growth occurs: the doubling time or the initial amount? Use the results from #1 and #2 to justify your answer. Part #2: Doubling Time and Half-Life (10 points) 1. Thermonuclear weapons use tritium for their nuclear warheads. Tritium is a radioactive form of hydrogen (containing 1 proton and 2 neutrons) with a half-life of about 12 years. Suppose a nuclear warhead contains 1 kilogram of tritium. How much will remain in 50 years? Use your answer to explain why thermonuclear weapons require regular maintenance. In 50 years the warhead will contain .056 kg of tritium which is very small compared to the starting amount of 1 kilogram. Regular maintenance is required to keep the warhead at its maximum potential. No one would want their weapons to lose power over time. They are maintained in order to remain effective. 2. The homicide rate decreases at a rate of 3% per year in a city that had 800 homicides in the most recent year. At this rate, in how many years will the number of homicides reach 400 in a year? It will take 23.3 years for the number of homicides to reach 400 in a year. 3. The Consumer Price Index (CPI) is increasing at a rate of 3% per year. What is its doubling time? By what factor will prices increase in 3 years? 4. Oil consumption is increasing at a rate of 2.2% per year. What is its doubling time? By what factor will prices increase in 1 year? In 8 years? Part #3: Population Growth (6 points) 1. Starting from the 7.1 billion world population in 2013, assume that world population maintains its current annual growth rate of 1.1%. What will be the world population in 2020? 2031? 2081? Part #4: Variation of Sound with Distance (8 points) 1. Suppose a siren is placed 0.1 meters from your car. Answer the following questions: How many times as loud as a siren at 30 meters will the sound you hear be? How loud will the siren next to your car sound, in decibels? How likely is it that this siren will cause damage to your eardrum? Explain. Part #5: Property Depreciation (10 points) 1. Go to IRS website, and examine the rules for depreciation of some type of property, such as a rental property or a piece of business equipment. Complete the following activities: Describe the type of property and what it would be used for. Make a linear model that describes the depreciation function. Based on the current price of the property, use the model to predict the value after 1 year? 5 years? 10 years? Part #6: Renewable Energy (10 points) 1. Find data on the power production from some source of renewable energy, such as wind or solar. Answer the following questions: Do you see evidence that production is increasing exponentially? Explain. Based on current trends, what can you predict about the future importance of this energy sources? Explain. Properly cite the source of your data