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# SI Notes MATH127

UMass

GPA 3.2

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## Popular in Calculus for Life and Social Problems I

## Popular in Mathematics (M)

This 3 page One Day of Notes was uploaded by Elena Bassin on Tuesday February 3, 2015. The One Day of Notes belongs to MATH127 at University of Massachusetts taught by Adena Calden in Spring2015. Since its upload, it has received 136 views. For similar materials see Calculus for Life and Social Problems I in Mathematics (M) at University of Massachusetts.

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Date Created: 02/03/15

fquot n 39 6 3353553 392 5 05 Karen Li quot v 39 WS SI Session r mm O 39 DD 3 Tuesday 830945 pm Math 127 Dubois Library 1367 Topics covered today 39 I Algebra review a1 Logs quot b Natural logs II Functions a Composite Functions b Graph Shifting c Periodic Functions III Rate of change a39 Average Rate of Change b Instantaneous Rate of Change 1 Algebra Review A Log rules 1 B Natural log rules 1 Q2J13 39e bum 1 itaibmiiogb 1 2 10 0 ml 1 imam 1030 okay quotquot i 39iu shm 4 Change of Base Fortnula I 1 10 ihe39 ex 099 ex 27 213 19M ht of 3 I o a Dim n l i as m m mm aw 1 Q0333 H 138 ii 1E3 i 3m mm 3 39 39 L Q goc in A 1 1 EMI izlhrl JPQMQQL Sine graph 912395 L 5 03qu Cosine Graph 3 mg no e quotii n I 25 cc 1 009 3 h R XV k 1 quot Sine and cosine graph are the same graph butjust shifted 3 Uquot Yx 11 What is a function 39 QRquot WNW M Calm NQW T 5 wk 39 7 CU i 3 ex 11Let W t represent coffee production in the state of Columbia in thousands of metric tons where t is years since 1990 Which of the following is the interpretation of the statement a 12 9 in terms of corn production A Kansas produced minceis tons of corn in 1999 Mh 1 Jk I i Kansas produced 9009 metric tons of corn in 2002 In anyquot N 391 e1 E Q 2 LQ Kansas produced 9 metric tons of corn in 2602 x 7 D Kansas produced 12000 metric tons of corn in 1999 W5 M 3m Mb E None of these wriner 5 WINE nfu r K A Composite functions Iggng at ggt gx ex 2 Let 1 43 11 and gng x I Which of the following is true Q 9 item 31Ic2 1x 12 965mm 35b quot 15 q Bfx sx3x 5x69 H u amt 5 C gf x 3x2 29x 69 35 5 Maw 6r 5 3931 ii9c393 156 7 Bud th i1 D gel fol 12x320x2 4x ex 3 Based on the table below which of the following is equivalent to gh 1 m 5 43 lt x 3 2 1 o 1 1 gx 0 C1 2 3 1 5 2 hx 3 0 2 4 1 is E None of these 3 Graph Shifting uh ex 4 Iigntify how you would move the graph of the lnction 39 3 kaob f x so it becomes the graph of quotl r 3 cquot 9L 3 gex 12s h J 39 E h 95 ows t one unit right and ve units up quot J 5 WIN 1 T a if ww BEEFNilth one unit right and ve units down a 39 39 C five unit left and one unit up 39 l3 Ptx g E Wekath so mnznllnlts u D ve unit left and one unit down i E None of these do b 39PLXquot a H lat ec l L C Periodic Functions Amplitude 2 mm 2 who ovum 7 39 339 lhzoCEJtAvg Period a 39 339 gets CEonc Vertical shift C2 WW ex 5 Find a formula for the following graph 1mm o9 wham owa Q n we untilwe A y 7 Sin t 1 er in n Ry10cos Quito MD WEE quot g t y73in 31ch 9459 MOL my 76053 W 5 73h trig ex 6a Delta Cephei is one of the most visible stars in the hi I sky Its brightness has eriods of 64 da htheiaxerage I ll mess 3 oi elta Cephei as Q Pawn 33 31 13 nqtbs UH 152 ggg 1 3 has quot on 14 4 bq m s Wm Ll 3395 I 3 ex 613 extra A person breathes in and out eveg ve seconds The Volume of airin the person39s lungs varies between a minimum of 2 Liters and a WWW Which of the following is the best formula for thelvolume ofair in the person39s lungs as a function of time nal 5 gt 23 5g Wl h 5 luuu ney 1 5 r meZ l I g otv v W ebnvms E on a2 sears s 12 1 quot quotz 2quot J 1 111 Rate of Change A Average Rate of Change Graphically the line connecting two points on a graph is called the FROG Uta Whenever you see average rate of change 9 90quot with lend 39 ex 7 Height of the ball is modeled by 20 t where t is measured in seconds Find Average yelocity from t0 to F4 elm elm a e was 041 ex 8 The table below shows the total amount spent in billions of dollars on tobacco products in the US Find the average e ount s end on tobacco roducts between 1987 and 1993 Year 1937 1988 1989 1990 1991 1992 1993 Spending 356 362 405 434 454 509 505 FM ae mum mm Answer 25 billion dollars per year b 4 WW3 www don39t forget umts f 39quot BSL7 ZJSM39A RT ex 9 W of change for the mction y 21110 between x 1 and x 2 rounded to 2 decimals A 133 D B 177 39 130 italquot 9C 21 Lowem0 C 127 r quot D 069 0 7 139 29 3923 3 l 5 B Instantaneous Rate of Change How much a function changes at one point Graphically we are looking at the m When you see best estimate instantaneous f n quot nd the average rate of change to the in li andgn39glll of the value 03 N mm a we but lKQ39 firmme mtg LT quotacDA 392 ex 10 Estimate P 0 ifPt 300108 W mm if 9 Q 13ODL10 5i Wquot atom hemmucous tale at pm We A 32 W Vallth P 0 emote lo 33929 2 13913 2 W 23415 1 t n ex 11 The table below gives total sales of candy ct in millions of dollars as a function of the year t Which of the following is the best estimate for c 1998 Year t 1996 1997 1998 1999 2000 candy sales C12 6621 7739 3470 9425 8033 e a q atlutt 4130 409 million dollars per year C qule L 818 million dollars per year 1 19101quot Wickl 2 C 1362 million dollars per year W cg D 1904 million dollars per year Do not solve for the derivative for a problem like in example 10 it says estitna

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