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1 | (88) |
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2 | (6) |
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8 | (8) |
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1.3 Average Rate Of Change And Relative Change |
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16 | (12) |
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1.4 Applications Of Functions To Economics |
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28 | (11) |
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1.5 Exponential Functions |
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39 | (7) |
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1.6 The Natural Logarithm |
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46 | (5) |
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1.7 Exponential Growth And Decay |
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51 | (9) |
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1.8 New Functions From Old |
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60 | (5) |
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1.9 Proportionality And Power Functions |
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65 | (6) |
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71 | (18) |
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78 | (6) |
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Strengthen Your Understanding |
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84 | (2) |
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Projects: Compound Interest, Population Center Of The Us, Medical Case Study: Anaphylaxis |
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86 | (3) |
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2 Rate Of Change: The Derivative |
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89 | (48) |
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2.1 nstantaneous Rate Of Change |
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90 | (7) |
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2.2 The Derivative Function |
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97 | (6) |
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2.3 Interpretations Of The Derivative |
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103 | (9) |
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2.4 The Second Derivative |
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112 | (6) |
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2.5 Marginal Cost And Revenue |
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118 | (19) |
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124 | (4) |
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Strengthen Your Understanding |
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128 | (1) |
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Projects: Estimating Temperature Of A Yam; Temperature And Illumination; Chlorofluorocarbons In The Atmosphere |
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129 | (2) |
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131 | (1) |
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Limits, Continuity, And The Definition Of The Derivative |
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131 | (6) |
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3 Shortcuts To Differentiation |
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137 | (38) |
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3.1 Derivative Formulas For Powers And Polynomials |
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138 | (7) |
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3.2 Exponential And Logarithmic Functions |
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145 | (5) |
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150 | (6) |
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3.4 The Product And Quotient Rules |
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156 | (5) |
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3.5 Derivatives Of Periodic Functions |
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161 | (14) |
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165 | (3) |
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Strengthen Your Understanding |
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168 | (1) |
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Projects: Coroner's Rule Of Thumb; Air Pressure And Altitude; Relative Growth Rates: Population, Gdp, And Gdp Per Capita; Keeling Curve: Atmospheric Carbon Dioxide |
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169 | (2) |
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171 | (1) |
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Establishing The Derivative Formulas |
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171 | (3) |
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174 | (1) |
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175 | (66) |
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4.1 Local Maxima And Minima |
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176 | (7) |
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183 | (6) |
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4.3 Global Maxima And Minima |
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189 | (5) |
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4.4 Profit, Cost, And Revenue |
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194 | (8) |
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202 | (6) |
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208 | (5) |
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213 | (8) |
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4.8 The Surge Function And Drug Concentration |
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221 | (20) |
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228 | (7) |
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Strengthen Your Understanding |
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235 | (2) |
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Projects: Average And Marginal Costs, Firebreaks, Production And The Price Of Raw Materials, Medical Case Study: Impact Of Asthma On Breathing |
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237 | (4) |
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5 Accumulated Change: The Definite Integral |
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241 | (50) |
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5.1 Distance And Accumulated Change |
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242 | (8) |
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5.2 The Definite Integral |
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250 | (5) |
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5.3 The Definite Integral As Area |
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255 | (5) |
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5.4 Interpretations Of The Definite Integral |
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260 | (8) |
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5.5 Total Change And The Fundamental Theorem Of Calculus |
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268 | (4) |
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272 | (19) |
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276 | (5) |
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Strengthen Your Understanding |
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281 | (2) |
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Projects: Carbon Dioxide In Pond Water, Flooding In The Grand Canyon |
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283 | (4) |
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287 | (1) |
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Theorems About Definite Integrals |
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287 | (4) |
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6 Antiderivatives And Applications |
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291 | (40) |
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6.1 Analyzing Antiderivatives Graphically And Numerically |
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292 | (5) |
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6.2 Antiderivatives And The Indefinite Integral |
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297 | (5) |
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6.3 Using The Fundamental Theorem To Find Definite Integrals |
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302 | (4) |
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6.4 Application: Consumer And Producer Surplus |
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306 | (6) |
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6.5 Application: Present And Future Value |
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312 | (4) |
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6.6 Integration By Substitution |
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316 | (5) |
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321 | (10) |
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324 | (2) |
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Strengthen Your Understanding |
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326 | (2) |
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Projects: Quabbin Reservoir, Distribution Of Resources, Yield From An Apple Orchard |
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328 | (2) |
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330 | (1) |
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331 | (22) |
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332 | (4) |
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7.2 Cumulative Distribution Functions And Probability |
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336 | |
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7.3 The Median And The Mean |
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34 | (319) |
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348 | (2) |
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Strengthen Your Understanding |
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350 | (1) |
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Projects: Triangular Probability Distribution |
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351 | (2) |
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8 Functions Of Several Variables |
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353 | (56) |
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8.1 Understanding Functions Of Two Variables |
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354 | (4) |
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358 | (11) |
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369 | (7) |
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8.4 Computing Partial Derivatives Algebraically |
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376 | (5) |
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8.5 Critical Points And Optimization |
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381 | (6) |
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8.6 Constrained Optimization |
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387 | (22) |
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394 | (5) |
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Strengthen Your Understanding |
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399 | (2) |
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Projects: A Heater In A Room, Optimizing Relative Prices For Adults And Children, Maximizing Production And Minimizing Cost: "Duality" |
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401 | (2) |
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403 | (1) |
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Deriving The Formula For A Regression Line |
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403 | (6) |
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9 Mathematical Modeling Using Differential Equations |
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409 | (54) |
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9.1 Mathematical Modeling: Setting Up A Differential Equation |
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410 | (4) |
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9.2 Solutions Of Differential Equations |
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414 | (4) |
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418 | (6) |
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9.4 Exponential Growth And Decay |
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424 | (6) |
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9.5 Applications And Modeling |
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430 | (9) |
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9.6 Modeling The Interaction Of Two Populations |
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439 | (6) |
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9.7 Modeling The Spread Of A Disease |
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445 | (18) |
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450 | (2) |
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Strengthen Your Understanding |
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452 | (3) |
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Projects: Harvesting And Logistic Growth, Population Genetics, The Spread Of Sars |
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455 | (3) |
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458 | (1) |
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458 | (5) |
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463 | (20) |
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464 | (6) |
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10.2 Applications To Business And Economics |
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470 | (4) |
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10.3 Applications To The Natural Sciences |
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474 | (9) |
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479 | (1) |
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Strengthen Your Understanding |
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480 | (1) |
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Projects: Do You Have Any Common Ancestors?, Harrod-Hicks Model Of An Expanding National Economy, Probability Of Winning In Sports, Medical Case Study: Drug Desensitization Schedule |
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481 | (2) |
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483 | (24) |
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A Fitting Formulas To Data |
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484 | (8) |
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B Compound Interest And The Number E |
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492 | (5) |
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497 | (10) |
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1 Malthus: Population Outstrips Food Supply |
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497 | (1) |
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498 | (1) |
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499 | (1) |
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4 Comparing Home Mortgages |
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500 | (1) |
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5 Present Value Of Lottery Winnings |
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501 | (1) |
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501 | (1) |
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7 Investing For The Future: Tuition Payments |
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502 | (1) |
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502 | (1) |
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9 Verhulst: The Logistic Model |
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503 | (1) |
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10 The Spread Of Information: A Comparison Of Two Models |
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504 | (1) |
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11 The Flu In World War I |
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504 | (3) |
Answers To Odd-Numbered Problems |
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507 | (28) |
Pretest |
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535 | (4) |
Index |
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539 | |