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Chapter 3 20

# Chapter 3 20 - 170 CHAPTER 3 DIFFERENTIATION RULES C 6 —...

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Unformatted text preview: 170 CHAPTER 3 DIFFERENTIATION RULES . C 6 — C 2 0.0295 — 0.0570 A . 22. (a) (I) M : —— (b) Slope : —C m #M m 70.01 (moles/L)/min 6 — 2 4 = 70.006875 (moles/L)/min C(t) C(4) ~ 0(2) 0.0408 — 0.0570 0-08 4 — 2 2 0.06 : —0.008 (moles/[J/min C(2) # 0(0) 0.0570 — 0.0800 004 ('1') 2 — 0 : 2 = —0.0115 (moles/L)/min 1860 7 1750 2070 1 1860 23. 1920: _ 1m _ gm _ (3) m1 1920 1 1910 10 11‘7”? 1930 4 1920 10 21’ (m1 —— m2)/ 2 = (11 —— 21)/2 = 16 million/year 4450 4 3710 5280 — 4450 1980: 4 L40 ‘ _ w 1 m 1980 — 1970 10 74m? 1990 — 1980 10 83‘ (m1 —— m2)/ 2 = (74 _- 83)/2 : 78.5 million/year (b) P(t) : at3 + bt2 + ct + d (in millions of people). where a % 00012937063, 12 % —7.061421911, c % 12,822.97902. and d % 77.743.770.396. (c) P(t) : at3 + bt2 + at + d => P'(t) : 3at2 + 2bt + c (in millions of people per year) (d) P'(1920) : 3(00012937063)(1920)2 + 2(—7.061421911)(1920) + 12.822.97902 % 14.48 million / year [smaller than the answer in part (a). but Close to it] P’(1980) % 75.29 million/year (smaller. but close) (e) P'(1985) a: 81.62 million / year. so the rate of growth in 1985 was about 81.62 million/year. 24. (a) A(t) : at4 + 5:3 + 0152 + dt —— e. where a : —5.8275058275396 x 10-61) : 0.0460458430461. c : ~136.43277039706.d : 17966102676871. and e = ~88.717,597.060767. (b) A(t) : at4 + 57:3 + ct2 + dt -— e :> A’(t) : 4m3 + 3bt2 + 2ct + d (c) A’(1990) m 0.0833 years of age per year ((1) 26 25 24 23 03 02 01 0_ 701 1955 1965 1975 1985 1995 1950 1960 1970 1980 1990 ...
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