Data about recent federal defense spending are given in the accompanying Statistical Abstract of the United States table. Here t denotes the time, in years, since 1990 and D denotes federal defense spending, in billions of dollars D- Spending (billions of dollars) t = Years since 1990 328.4 310.0 10 341.5 565.5 843.8 20 (a) Calculate the average yearly rate of change in defense spending from 1990 to 1995. billion dollars per year (b) Use your answer from part (a) to estimate D(3). billion dollars Explain what this value means. O D(3) is the federal defense spending for 1903, in billions of dollars. O D(3) is the average rate of change in federal defense spending from 1990 to 1993, in billions of dollars. O D(3) is the percent increase in federal defense spending from 1990 to 1993, in billions of dollars. O D(3) is the percent increase in federal defense spending from 1900 to 1903, in billions of dollars. O D(3) is the federal defense spending for 1993, in billions of dollars. (c) Calculate the average yearly rate of change in defense spending from 2005 to 2010. billion dollars per year (d) Use your answer from part (c) to estimate the value of D(22). billion dollars
Data about recent federal defense spending are given in the accompanying Statistical Abstract of the United States table. Here t denotes the time, in years, since 1990 and D denotes federal defense spending, in billions of dollars D- Spending (billions of dollars) t = Years since 1990 328.4 310.0 10 341.5 565.5 843.8 20 (a) Calculate the average yearly rate of change in defense spending from 1990 to 1995. billion dollars per year (b) Use your answer from part (a) to estimate D(3). billion dollars Explain what this value means. O D(3) is the federal defense spending for 1903, in billions of dollars. O D(3) is the average rate of change in federal defense spending from 1990 to 1993, in billions of dollars. O D(3) is the percent increase in federal defense spending from 1990 to 1993, in billions of dollars. O D(3) is the percent increase in federal defense spending from 1900 to 1903, in billions of dollars. O D(3) is the federal defense spending for 1993, in billions of dollars. (c) Calculate the average yearly rate of change in defense spending from 2005 to 2010. billion dollars per year (d) Use your answer from part (c) to estimate the value of D(22). billion dollars
Linear Algebra: A Modern Introduction
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ISBN:9781285463247
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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Transcribed Image Text:Data about recent federal defense spending are given in the accompanying Statistical Abstract of the United States table. Here t denotes the time, in years, since 1990 and D denotes federal defense spending, in billions of dollars.
D = Spending
(billions of dollars)
328.4
t = Years since 1990
5
310.0
10
341.5
565.5
15
20
843.8
(a) Calculate the average yearly rate of change in defense spending from 1990 to 1995.
billion dollars per year
(b) Use your answer from part (a) to estimate D(3).
billion dollars
Explain what this value means.
O D(3) is the federal defense spending for 1903, in billions of dollars.
O D(3) is the average rate of change in federal defense spending from 1990 to 1993, in billions of dollars.
O D(3) is the percent increase in federal defense spending from 1990 to 1993, in billions of dollars.
O D(3) is the percent increase in federal defense spending from 1900 to 1903, in billions of dollars.
O D(3) is the federal defense spending for 1993, in billions of dollars.
(c) Calculate the average yearly rate of change in defense spending from 2005 to 2010.
billion dollars per year
(d) Use your answer from part (c) to estimate the value of D(22).
billion dollars
Expert Solution
Step 1
(a) To find the average yearly rate of change in defense spending from 1990 to 1995:
'
where,
r is the average yearly rate of change in defense spending.
D(5) is defense spending for 1995(t = 5 years from 1990) = $310.0 billion.
D(0) is defense spending for 1990(t = 0 years from 1990) = $328.4 billion.
n is the number of year = 5-0
n = 5.
Therefore,
Since amount cannot be negative.
r = $3.68 billion per year.
Thus, the average yearly rate of change in defense spending from 1990 to 1995 is $3.68 billion per year.
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