SOLUTION MANUAL FOR Applied Calculus 7th Edition by Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath ISBN: 978-1119799061 COMPLETE GUIDE ALL CHAPTERS COVERED 100% VERIFIED A+ GRADE ASSURED!!!!NEW LATEST UPDATE!!!!!

1.1 SOLUTIONS
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,2 Chapter One /SOLUTIONS dt dt




CHAPTER ONE dt




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1. (a) The story in (a) matches Graph (IV), in which the person forgot her books and had to return home.
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(b) The story in (b) matches Graph (II), the flat tire story. Note the long period of time during which the distance fr
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om home did not change (the horizontal part).
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(c) The story in (c) matches Graph (III), in which the person started calmly but sped up later.
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The first graph (I) does not match any of the given stories. In this picture, the person keeps going away from hom
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e, but his speed decreases as time passes. So a story for this might be: I started walking to school at a good pace, but since
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I stayed up all night studying calculus, I got more and more tired the farther I walked.
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2. The height is going down as time goes on. A possible graph is shown in Figure 1.1. The graph is decreasing.
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height




time

Figure 1.1 dt




3. The amount of carbon dioxide is going up as time goes on. A possible graph is shown in Figure 1.2. The graph is increasing.
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CO2




time

Figure 1.2 dt

, 1.1 SOLUTIONS
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4. The number of air conditioning units sold is going up as temperature goes up. A possible graph is shown in Figure 1.
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3. The graph is increasing.
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AC units
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temperature

Figure 1.3 dt




5. The noise level is going down as distance goes up. A possible graph is shown in Figure 1.4. The graph is decreasing.
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noise leveldt




distance

Figure 1.4 dt




6. If we let t represent the number of years since 1900, then the population increased between t = 0 and t = 40, stay
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ed approximately constant between t = 40 and t = 50, and decreased for t ≥ 50. Figure 1.5 shows one possible graph. M
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any other answers are also possible.
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population




years
20 d t d t 40 d t d t 60 d t d t 80 d t 100 120 since 1900
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dt




Figure 1.5 dt

, 4 Chapter One /SOLUTIONS dt dt




7. Amount of grass G = f (r) increases as the amount of rainfall r increases, so f (r) is an increasing function.
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8. We are given information about how atmospheric pressure P = f (ℎ) behaves when the altitude ℎ decreases: as altitude
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ℎ decreases the atmospheric pressure P increases. This means that as altitude ℎ increases the atmospheric pressure P
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decreases. Therefore, P = f (ℎ) is a decreasing function.
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t dt dt dt dt



9. We are given information about how battery capacity C = f (T ) behaves when air temperature T decreases: as T decrease
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s, battery capacity C also decreases. This means that increasing temperature T increases battery capacity C. Theref
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ore, C = f (T ) is an increasing function.
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t dt dt dt dt dt



10. Time T = f (m) increases as m increases, so f (m) is increasing.
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11. The attendance A = f (P ) decreases as the price P increases, so f (P ) is a decreasing function.
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t dt dt dt dt dt dt dt dt dt d
t dt dt dt dt dt



12. The cost of manufacturing C = f (v) increases as the number of vehicles manufactured v increases, so f (v) is an increasin
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g function.
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13. We are given information about how commuting time, T = f (c) behaves as the number of cars on the road c decrease
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s: as c decreases, commuting time T also decreases. This means that increasing the number of cars on the road c increa
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ses commuting time T . Therefore, T = f (c) is an increasing function.
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t dt dt dt dt



14. The statement f (4) = 20 tells us that W = 20 when t = 4. In other words, in 2019, Argentina produced 20 million metri
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c tons of wheat.
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15. (a) If we consider the equation
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C = 4T − 160
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simply as a mathematical relationship between two variables C and T , any T value is possible. However, if we thin
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k of it as a relationship between cricket chirps and temperature, then C cannot be less than 0. Since C = 0 lea
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ds to 0 = 4T − 160, and so T = 40 F, we see that T cannot be less than 40 F. In addition, we are told that the
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function is not defined for temperatures above 134 . Thus, for the function C = f (T ) we have
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t dt dt dt




Domain = All T values between 40 F and 134 F dt dt dt dt dt dt dt dt dt d t



= All T values with 40 ≤ T ≤ 134
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= [40, 134].
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(b) Again, if we consider C = 4T − 160 simply as a mathematical relationship, its range is all real C values. However
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, when thinking of the meaning of C = f (T ) for crickets, we see that the function predicts cricket chirps per mi
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nute between 0 (at T = 40 F) and 376 (at T = 134 F). Hence,
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Range = All C values from 0 to 376 dt dt dt dt dt dt dt dt



= All C values with 0 ≤ C ≤ 376
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= [0, 376].
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16. (a) The statement f (19) = 415 means that C = 415 when t = 19. In other words, in the year 2019, the concentration
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t dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt


of carbon dioxide in the atmosphere was 415 ppm.
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(b) The expression f (22) represents the concentration of carbon dioxide in the year 2022.
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17. (a) At p = 0, we see r = 8. At p = 3, we see r = 7.
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(b) When p = 2, we see r = 10. Thus, f (2) = 10. dt dt dt dt dt dt dt dt dt dt d
t dt dt



18. Substituting x = 5 into f (x) = 2x + 3 gives dt dt dt dt d t dt dt dt dt dt dt




f (5) = 2(5) + 3 = 10 + 3 = 13.
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t dt dt dt dt dt dt dt dt dt dt




19. Substituting x = 5 into f (x) = 10x − x2 gives dt dt dt dt d t dt dt dt dt dt dt




f (5) = 10(5) − (5)2 = 50 − 25 = 25.
d
t dt dt dt dt dt dt dt dt dt dt




20. We want the y-coordinate of the graph at the point where its x-coordinate is 5. Looking at the graph, we see that the
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y-coordinate of this point is 3. Thus dt dt dt dt dt dt


f (5) = 3. d
t dt dt