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Exponential February 21, 2005 Exponential Review Fill in the following table. Exponential Initial Value Function t Growth or Decay? Growth or Decay Factor Growth or Decay Rate A = 4(1.03) A = 10(0.98) t 1000 1.005 30 0.96 $50,000 Growth 7.05% 200 grams Decay 49% Applied Problem 1 The United States imported $495 billion worth of goods from abroad in 1990 and $912 billion worth of goods in 1998. a) Find a linear function of time since 1990. b) Describe the slope in context of the problem. c) Find an exponential function of time since 1990. d) Describe the growth rate in context of the problem. e) In 2003, the United State imported $1172 billion worth of goods. Which model best fits? Explain. Exponential February 21, 2005 Applied Problem 2 – On your own. In 1990, the United States produced $43 billion dollars of electronics and electronic components. In 1994, the United States produced $58.2 billion dollars. a) Find a linear function of time since 1990. b) Describe the slope in context of the problem. c) Find an exponential function of time since 1990. d) Describe the growth rate in context of the problem. e) In 1998, the United State produced $76 billion. Which model best fits? Explain. Exponential February 21, 2005 Applied problem 3 In 1798 an economist named Malthus argued that population size can be predicted from one year to the next by multiplying by a fixed amount. He also argued that food production can be predicted from one year to the next by adding a fixed quantity. The table below lists the world population in millions and food production in millions of “food units”. A food unit is the amount of food necessary to feed on person. Year World Population (millions) 980 1254.4 1605.6 1800 1850 1900 Food Production (millions of food units) 1200 1550 1900 a) Find the equation for the world population as a function of time. b) Find the equation for the food production as a function of time. c) According to the function that you found in part b), when will food production reach 6060 million food units? d) Based upon your equations, when will the world not have enough food? Homework p. 269 #19, 20, 21, 25, 27