Annual U.S. imports from a certain country in the years 1996 through 2003 can be approximated byI(t) + 3.6t+47 (1st s9)billion dollars, where t represents time in years since 1995. Annual U.S. exports to this country in the same years can be approximated byE(t) 0.5²-1.4t+16 (0 sts 10)billion dollars.Assuming the trends shown in the above models continue indefinitely, numerically estimate the following. (If an answer does not exist, enter DNE.)im E(t) and lim7-***lim e(t)-E(t)lim1-+= 1(1)-E(E)(1)

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Answered: Annual U.S. imports from a certain…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2) The Nikkei 225 index is a stock market index for the Tokyo Stock Exchange. The Nikkei 225 index for the period 1990-2010 can be modeled by V (t) = 23,500e-0.0381t where t is the number of years after 1990. Determine how many years after 1990 the Nikkei 225 index reached $20,000.
The demand for ceiling fans can be modeled below as D(p) = 25.62(0.996P) thousand ceiling fans where p is the price (in dollars) of a ceiling fan. (a) According to the model, is there a price above which consumers will no longer purchase fans? Explain why or why not. The model is exponential and ---Select--- ✓the horizontal axis. Therefore there ---Select--- above which consumers will not purchase a ceiling fan. (b) Calculate the amount that consumers are willing and able to spend to purchase 17 thousand ceiling fans. (Round your answer to three decimal places.) thousand (c) How many fans will consumers purchase when the market price is $100? (Round your answer to three decimal places.) thousand fans (d) Find the consumers' surplus when the market price is $100. (Round your answer to three decimal places.) thousand
Suppose the U.S. Census Bureau projects the population of Colorado to be 4.3 million in 2000 and 6.1 million in 2020. Assuming the population growth is linear, Use t years since 1999 and p the population of Colorado in millions. According to your linear model, what is the population of Colorado in 2033? {final answer will be decimal number with two decimal places only}
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According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model P(t) = 304 · (1.011)* - represents the population P (in millions of people) in year t. According to the model, when will the population be 407 million people? Be sure to round your answer to the nearest whole year. Year
13. In the year 1990, kids everywhere collected Beanie Babies. There was such a demand that these critters skyrocketed in value. Katie bought a Beanie Baby for $10.00. The stuffed animals' value increased at a rate of 7% per year. a) Write an exponential growth model for the value of the Beanie Baby in terms of the number of years since the purchase. b) What was the value of the Beanie Baby after 2 years? c) How much is it worth today? d) How long did it take for Katie to double her original investment?
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According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model t – 2008 P(t) = 304 · (1.011)* represents the population P (in millions of people) in year t. According to the model, when will the population be 366 million people? Be sure to round your answer to the nearest whole year. Year
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