1. Read each statement below and determine which can be represented by a linear function and which can be represented by an exponential function. For each, write the function that represents the situation. Statement 1: The value of the home increased by 2.5% each year. Its initial value was $150,000. Statement 2: The value of the home increased by $2500 each year. Its initial value was $150,000. 2. Aubrey bought a diamond ring for $8,000. If the value of the ring increases at a constant percent change rate of 4.25% per year, how much will the ring be worth in 20 years? Show your work. 3. Data regarding world energy consumption of alternative fuels (geothermal, solar, wind, wood, and waste) is listed in the table. (Source: Statistical Abstract of the United States, 2007, Table 1353) Year Energy Consumption (since 1990) (quadrillion BTU) E 0 1.7 5 2.2 9 2.8 10 3.0 11 3.1 12 3.4 13 3.7 14 3.9 a. Use exponential regression to find a model for the data set. (Round the parameters to 3 decimal places) E(y) = b. Using the model from part a, what is the projected world consumption for alternative fuels in 2010? (Round your answer to the nearest tenth).4. The number of farms, in thousands, with milk cows may be modeled by C() = 191.51(0.94) , where ? is the number of years since 1990. (Source : Statistical Abstract of the United States, 2007, Table 846) a. How many farms had milk cows in 1990? b. By what percent is the number of farms changing? c. Using logarithms determine the year when will there be 10 thousand farms with milk cows. d. Using mathematics, explain if there will ever be zero farms with milk cows. 5. According to the CIA World Factbook, the population of Iran was 66.4 million in July 2009 and was growing at a rate of 0.883% per year (Source: www.cia.gov). a. Create an exponential function model for the population of Iran / years after July 2009. b. Use the model in part (a) to forecast the July 2022 population of Iran. (Round to 3 decimal places) c. According to the model in part (a), in what year will the population of Iran reach 80.0 million? (Round to 3 decimal places) 6. True or false: log(2) = 2 . log(1). Justify your answer.7. The production of stone for use in construction is in the table. Source: Statistical Abstract of the United States, 2007, Table 874 Year Stone (since 1989) (million metric tons) S 1110 6 2420 11 2810 15 3050 16 3110 a. Draw a scatterplot and explain what the concavity of the scatterplot means in the real-life terms of the data. -4000 + Stone (million metric ton) -3000 2000 1000 10 15 20 Year (Since 1989) b. Use regression to find a logarithmic model (y,~a + b . In(x)) of best fit. (Round to 3 decimal places) S(y) = c. Predict the production of stone for construction in 2009. (Round to 3 decimal places)8. Based on data from 1990 to 2000, the percentage of the economy attributed to the information technology sector may be modeled as follows: P()= 2.956 1+30.15e-0.5219t + 7.9 where P is the percentage of the economy and t is the number of years since the end of 1990. (Source: Statistical Abstract of the United States, 2001, Table 1122) Approximate the rate at which the information technology percentage of the economy was changing at the end of 1999. (Hint: to estimate the percentage of change for year n, calculate the average rate of change AROC between year n and year n-1). 9.A Chicken Pox vaccine became widely available in the United States in 1995. a) According to the model, does the vaccine appear to be having an effect? b) If the Lower Limit is 15 (thousand), what is the Logistic model? Hint: You must adjust the data. Years Since Reported Cases of 1985 Chicken Pox T (Thousands) C 0 178.2 5 173.1 10 120.6 14 46 16 22.5 18 20.9 c) Should there be a lower limit? Without a lower limit, would you expect chicken pox to be eradicated? Explain