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Avery Wilson Finance Project 3 1. Coroner's Rule of Thumb - Coroners estimate time of death using the rule of thumb that a body cools about 2F during the rst hour after death and about 1F for each additional hour. Assuming an air temperature of 68F and a living body temperature of 98.6F, the temperature Ht) in F of a body at a time 1' hours since death is given by T(t) = 68 + 30.65\". (a). For what value of k will the body cool by 2F in the rst hour? (b). Using the value of k found in part (a), after how many hours will the temperature of the body be decreasing at a rate of 1F per hour? (0). Using the value of k found in part (a), show that, 24 hours after death, the coroner's rule of thumb gives approximately the same temperature as the formula. 2. Relative Growth Rates: Population, GDP, and GDP per Capita (a). Let Y be the world's annual production (GDP). The world GDP per capita is given by Y/P where P is world population. Figure 3.27 shows relative growth rate of GDP and GDP per capita for 1952-2000.19 relative growth rate per year 8% World GDP 6% 4% 2% World GDP per capita 0% year 1950 1960 1970 1980 1990 2000 Figure 3.27 (i). Explain why the vertical distance between the two curves gives the relative rate of growth of the world population. (ii). Estimate the relative rate of population growth in 1970 and 2000. (b). In 2006 the relative rate of change of the GDP in developing countries was 4.5% per year, and the relative rate of change of the population was 1.2%. What was the relative rate of change of the per capita GDP in developing countries