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Answer to worksheet 3.3 and 3.4 1. The value of a painting is increasing exponentially and satisfies the differential equation where t is measured in years and P ( t ) is the value of the painting in millions of dollars. Use the differential equation to determine how fast the value will be increasing when the value reaches \$5 million. Write your answer in a sentence, and use appropriate units. P ( t ) = .08(5) = .4 When the painting’s value reaches \$5 million, the value will be increasing at a rate of \$.4million (\$400,000) per year. 2. The United States federal budget submitted by President Clinton for 2000 was \$1.8 trillion. The United States federal budget submitted by President Bush for 2005 was \$2.4 trillion. Assume that the United States federal budget grows at a rate proportional to its size and let the year 2000 correspond to t = 0. (a) Find the growth constant k correct to four decimal places for this situation. P

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