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chapter 1 56 - 56 U CHAPTER1 FUNCTlONS AND MODELS 21 30...

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Unformatted text preview: 56 U CHAPTER1 FUNCTlONS AND MODELS 21. 30 Many models appear to be plausible. Your choice depends on whether you think medical advances will keep increasing life expectancy. or if there is bound to he a natural leveling—off of life expectancy. A linear model. y : 0.24031: ~ 423.4818 gives us an estimate of 77.0 years for the year 2010. |890 20|0 45 22. (a) Let .1' denote the number of toaster ovens produced in one y (cost) week and y the associated cost. Using the points 12000 (1000: 9000) and (1500. 12.000). we get an equation of a 9000 12.000 — 9000 1500 — 1000 y : 0 (.r — 1000) + 9000 e y = 6:10 + 3000. y : 6x + 3000 6000 line: y 7 9000 : (r — 1000) :> 3000 500 1000 1500 2000 X (toaster ovens) (b) The slope of 6 means that each additional toaster oven produced adds $6 to the weekly production cost. (c) The y-intercept of 3000 represents the overhead costfthe cost incurred without producing anything. 23. We need to know the value of 1‘ such that f(.7c) : 21> +1111 : 2. Since :0 : 1 gives us y : 2, f’1(2) : 1. ., 1 . , 1 24.y:21:1.Interchangingxandygwesusx:Lil/31:1 :> 2Iy+at:y+1 => 2xy-yz17x : 1 “2171):171‘. :> 'y:2£_1:f 1(I) 25' (1 I” (21113 (61113)2:32:9 (b) 10g“) 25 +1ogm 4 : log10(25 ‘ 11) : 10g“, 100 : log“) 102 : 2 s0 . 1 (c) tan(arcsu1 5) : tang : ((1) Let 0 : C0521 —: 30(050 ’ Then. sin(cos 3) - sinfi- # V17 cos2 :‘/1(%)2 597 If; 26. (a) e” : 5 :> .r‘ : 111;) (b) 111 .1‘ : 2 :> .1: : 62 (c) (3'3” : 2 :> L5” : 1112 :> .I' : 111(1112) (d) tan’1 1' : 1 :> tailta1121.17:tanl i .1: : tan 1 (x 1.5574) 27. (a) After 4 days. % gram remains: after 8 days. $1 g: after 12 days i g; after 16 days. fi g. 1 1 . 1 , . 1 ‘ _ t/4 lb) 112(1) : 5‘ m(8) : 2—2 m(12) : 23 m(1()) : 34. From the pattern. we see that m(t)- ——2t/4. or 2 . (c) m : 2"”4 :> log.) m : 't/4 :> t : r1log2 m: this is the time elapsed when there are m grams of 1°”Pd. 1110.01 ((1) m : 0.01 r? t: #1log2001: #4 1‘12 > m 26.6 days ...
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