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Global Defense Spending The following table gives the projected global defense spending (in trillions of dollars) from the beginning of 2008 ( t = 0) through 2015 ( t = 7): Year, t 0 1 2 3 4 5 6 7 Spending, y 1.38 1.44 1.49 1.56 1.61 1.67 1.74 1.78 a. Find an equation of the least-squares line for these data. b. Use the result of pan (a) to estimate the rate of change in the projected global defense spending from 2008 through 2015. c. Assuming that the trend continues, what will the global spending on defense be in 2018?

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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
Publisher: Brooks Cole
ISBN: 9781285464640

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BuyFindarrow_forward

Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
Publisher: Brooks Cole
ISBN: 9781285464640
Chapter 8.4, Problem 26E
Textbook Problem
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Global Defense Spending The following table gives the projected global defense spending (in trillions of dollars) from the beginning of 2008 (t = 0) through 2015 (t = 7):

Year, t 0 1 2 3 4 5 6 7
Spending, y 1.38 1.44 1.49 1.56 1.61 1.67 1.74 1.78
  1. a. Find an equation of the least-squares line for these data.
  2. b. Use the result of pan (a) to estimate the rate of change in the projected global defense spending from 2008 through 2015.
  3. c. Assuming that the trend continues, what will the global spending on defense be in 2018?

a.

To determine

To find: The equation of least-squares line.

Explanation of Solution

Given:

The given data is,

Year(t)01234567
Spending(y)1.381.441.491.561.611.671.741.78

Formula used:

Suppose that there are n data points P1(x1,y1),P2(x2,y2),P3(x3,y3)Pn(xn,yn) .

Then, the least-squares line for the given data is given by linear equation y=mx+b .

The constants m and b satisfy the normal equations,

(x12+x22+x32++xn2)m+(x1+x2+x3++xn)b=x1y1+x2y2+x3y3++xnyn (1)

And,

(x1+x2+x3++xn)m+nb=y1+y2+y3++yn (2)

Calculation:

From the given data, it is observed that x=0 corresponds to 2008.

Form the new table is as shown below,

x01234567
y1.381.441.491.561.611.671.741.78

That is, x1=0,x2=1,x3=2,x4=3,x5=4,x6=5,x7=6,x8=7 and

y1=1.38,y2=1.44,y3=1.49,y4=1.56,y5=1.61,y6=1.67,y7=1.74,y7=1.78 .

Thus observe that n=7 .

Substitute the data points in the normal equation (1) and obtain as,

[(02+12+22+32+42+52+62+72)m+(0+1+2+3+4+5+6+7)b]=[(0)(1.38)+(1)(1.44)+(2)(1

b.

To determine

To estimate: The rate of change in the projected global defense spending from 2008 through 2015.

c.

To determine

To find: The expected global spending on defense in 2018.

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Chapter 8 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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How is...Ch. 8.6 - Suppose g1 and g2 are continuous and g1 (x) g2...Ch. 8.6 - PRINTED BY: f0988ba0c4e090b@ placeholder....Ch. 8.6 - What is the average value of f(x, y) over the...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 1-25. evaluate the double integral...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 34-41, find the volume of the solid...Ch. 8.6 - In Exercises 34-41, find the volume of the solid...Ch. 8.6 - In Exercises 34-41, find the volume of the solid...Ch. 8.6 - In Exercises 34-41, find the volume of the solid...Ch. 8.6 - In Exercises 34-41, find the volume of the solid...Ch. 8.6 - In Exercises 34-41, find the volume of the solid...Ch. 8.6 - In Exercises 34-41, find the volume of the solid...Ch. 8.6 - In Exercises 34-41, find the volume of the solid...Ch. 8.6 - In Exercises 42-47, find the average value of the...Ch. 8.6 - In Exercises 42-47, find the average value of the...Ch. 8.6 - In Exercises 42-47, find the average value of the...Ch. 8.6 - In Exercises 42-47, find the average value of the...Ch. 8.6 - In Exercises 42-47, find the average value of the...Ch. 8.6 - In Exercises 42-47, find the average value of the...Ch. 8.6 - Population Density of a Coastal Town The...Ch. 8.6 - Average Population Density of a Coastal Town Refer...Ch. 8.6 - Population Density Of A City The population...Ch. 8.6 - Average Profit The Country Workshops total weekly...Ch. 8.6 - Average Price of Land The rectangular region R...Ch. 8.6 - In Exercises 53-56, determine whether the...Ch. 8.6 - In Exercises 53-56, determine whether the...Ch. 8.6 - In Exercises 53-56, determine whether the...Ch. 8.6 - In Exercises 53-56, determine whether the...Ch. 8 - Fill in the blanks. 1. The domain of a function f...Ch. 8 - Fill in the blanks. 2. If the function f has rule...Ch. 8 - Fill in the blanks. 3. The graph of a function f...Ch. 8 - Fill in the blanks. 4. The trace of the graph...Ch. 8 - Fill in the blanks. 5. The partial derivative fx...Ch. 8 - Fill in the blanks. 6. The number fx(a, b)...Ch. 8 - Fill in the blanks. 7. A function f(x, y) has a...Ch. 8 - Fill in the blanks. 8. A critical point of f(x, y)...Ch. 8 - Fill the blanks. 9. By plotting the points...Ch. 8 - Fill in the blanks. 10. The method of Lagrange...Ch. 8 - Fill in the blanks. 11. If f(x, y) is continuous...Ch. 8 - Fill in the blanks. 12. The integral Rf(x,y)dA is...Ch. 8 - Let f(x,y)=xyx2+y2. Compute f(0, 1), f(1, 0), and...Ch. 8 - Let f(x, y) = f(x,y)=xey1+lnxy. Compute f(1, 1),...Ch. 8 - Leth (x, y, z) = xyez + xy. Compute h( 1, 1, 0),...Ch. 8 - Find the domain of the function f (u, v) = uuv.Ch. 8 - Find the domain of the function f (x, y) = xyx+y.Ch. 8 - Find the domain of the function f(x,y)=xy+y1xCh. 8 - Find The domain of the function...Ch. 8 - In Exercises 8-11, sketch the level curves of the...Ch. 8 - In Exercises 8-11, sketch the level curves of the...Ch. 8 - In Exercises 8-11, sketch the level curves of the...Ch. 8 - In Exercises 8-11, sketch the level curves of the...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 12-21, compute the first partial...Ch. 8 - In Exercises 22-27, compute the second-order...Ch. 8 - In Exercises 22-27, compute the second-order...Ch. 8 - In Exercises 22-27, compute the second-order...Ch. 8 - In Exercises 22-27, compute the second-order...Ch. 8 - In Exercises 22-27, compute the second-order...Ch. 8 - In Exercises 22-27, compute the second-order...Ch. 8 - Let f(x, y, z) = x3 + y2z + xy2z + 3xy 4z....Ch. 8 - In Exercises 29-34, find the critical point(s) of...Ch. 8 - In Exercises 29-34, find the critical point(s) of...Ch. 8 - In Exercises 29-34, find the critical point(s) of...Ch. 8 - In Exercises 29-34, find the critical point(s) of...Ch. 8 - In Exercises 29-34, find the critical point(s) of...Ch. 8 - In Exercises 29-34, find the critical point(s) of...Ch. 8 - In Exercises 35-38, use the method of Lagrange...Ch. 8 - In Exercises 35-38, use the method of Lagrange...Ch. 8 - Find the maximum and minimum values of the...Ch. 8 - Find the maximum and minimum values of the...Ch. 8 - In Exercises 39-42, evaluate the double integrals....Ch. 8 - In Exercises 39-42, evaluate the double integrals....Ch. 8 - In Exercises 39-42, evaluate the double integrals....Ch. 8 - In Exercises 39-42, evaluate the double integrals....Ch. 8 - In Exercises 43 and 44, find the volume of the...Ch. 8 - In Exercises 43 and 44, find the volume of the...Ch. 8 - Find the average value of The function f(x, y) =...Ch. 8 - IQs The IQ (intelligence quotient) of a person...Ch. 8 - Revenue Functions A division of Ditton Industries...Ch. 8 - Demand for CD Players In a survey concluded by...Ch. 8 - Average Daily TV-Viewing Time The following data...Ch. 8 - Female Life Expectancy at 65 The projections of...Ch. 8 - Mobile Phone Use in China The number of mobile...Ch. 8 - Maximizing Revenue Odyssey Travel Agencys monthly...Ch. 8 - Maximizing the Weigh is of Fish A pond is slacked...Ch. 8 - COBB-DOUGLAS PRODUCTION FUNCTIONS The production...Ch. 8 - COBB-DOUGLAS PRODUCTION FUNCTION Show that the...Ch. 8 - Find the domain of f(x,y)=x+y(1x)(2y)Ch. 8 - Find the first and second partial derivatives of...Ch. 8 - Find the relative extrema, if any, of f(x, y) =...Ch. 8 - Find the equation of the least-squares line for...Ch. 8 - Use the method of Lagrange multipliers to find the...Ch. 8 - Evaluate R(1xy)dA, where R is the region bounded...

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