1105_LW2_solutions_F11

1105_LW2_solutions_F11 - MAC1105 Lecture Worksheet 2...

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Unformatted text preview: MAC1105 Lecture Worksheet 2 Sections 2.1, 2.2, 2.5 Fall, 2011 l. (2.1) Delbert is offered a sales job that pays \$1000 per month plus 6% commission on his sales. Let I represent Delbert’s total monthly income for S dollars in monthly sales. Monthly Sales, S Total Monthly Income,l a) Complete this table for Delbert’s total monthly income on monthly sales of \$0, \$2000, \$4000, \$6000, \$8000, and \$10,000. we. age into, and moo warmer? 6% 200015 @120\) and lDDOM-ZQ is itlzo, ‘ Anal :0 m”, b) Write an algebraic equation that expresses I Delbert’s monthly income, I, as a function of his monthly sales, S. Graph this equation. Use a clearly labeled numerical scale on each axis, and label each axis to show which variable it represents. Which is the independent variable, IorS? ,3 I loco-l” 0.0m Income ‘in Do] lars c) From your graph, estimate the monthly sales .numawww for which Delbert’s monthl income is \$l500. _, 'mmea'S—‘mgwmgw 2000 4090 6000 3000 10000 12600 Then use your eq;a(tlorf rom part a) to ﬁnd the 5,1,, in Donm a1 gebraically. exact sales @11- 3‘! we“! I l .5750 5‘00 3: [000+ 0.095 Graphic estimate: 5 z 3L 5-00 5 Droégs Algebraic Exact Result: 8 =\$ 3?) S 2 £92.42: 3.3% not» 83 3 (1) Write sentences that interpret the slope and vertical intercept of the graph. Siopeﬂ. Delbarl,‘5 Monl'ihlj uncome/ ‘IﬂCfgﬂggé am average, 0'? “Raf” 3&6)?“ attachl-l-‘lamohﬂ dollar“ o€mgnil9ij gala)“, Vecilwﬂm ‘mlﬂocefl'l Ii- "Delberi’ Makes ho Sales ‘m a manila 7 [ms Momihlj Magma Wtu be ﬁlomﬁ. l 2. (2.2) Parts I—III are review from Intermediate Algebra. For all parts of this question, refer to the ﬁgure shown. ' Assume that line 1 is vertical and line 2 is horizontal. -—2 ~ w‘t I. The equation ofline 1 is \“Ml 3i gl°Per a: “T” Lm a) x = —l b) y = —1 c) y = —%x i e) y = 3 )lslnleféafl" . . :s (are) _8 II. The slope of km 2 IS ' b) —4 b) 4 i c) undeﬁned (no slope) d) —% III. The equation of line 3 is 1 “W” c)y=_1xm4 gin—43:41 c)y=——4x d) y=—4x—1 e) y=4x~4 Facts: Parallel lines have equal slopes. Perpendicular lines have negative reciprocal slopes. Or equivalently, the product of the slopes of two perpendicular lines is —1. “an, s slope "is 'w-Li)‘ so 'Ferp. ﬁlofse, its Vii. IV. The slope of any line perpendlcular to line 3 is d) —4 b) 4 c) undeﬁned (no slope) (1) mi— e) i 3. (2.1-2.2) At 4 months old a baby boy weighs 11.2 pounds, and by 7 months the boy weighs 15.1 I pounds. Let y = the boy’s weight (in pounds) at age .1: months a) Write a formula for a linear function that gives this bey’s weight as a function of his age, lens-2») (war) (it; “32) ‘X\ 3! Kb yk Answer: y: (‘7 15-0 «slope the Usiwﬂ “po‘m‘l‘” Slope g‘Wm” “' 37gb?“ 571.9% 3 m(pw;{!) We” L3 K/s n.2, tape-w 4») yam: 2:: Lawn 1)) Complete this sentence: ‘ yﬁ InBX 4*“(9 The equation in part a) suggests that this boy weighed C9 pounds at birth, and his weight is Whore/G45 in at an average rate of I. ‘3 up - _ re Manila .. ( increasing or decreasing ? ) ‘ (numerical answer) (correct units r this rate) 4. (2.1) Linear Regression The table and graph below illustrate how the number of on—the-air TV stations in the US. has increased since 1950. . Number of U.S. On—Aiz TV Stations y 25 38 35 48 15 Tine {years from 19503 a) Use the calculator to camr out linear regression on the (x,y) data in the table. Do not enter calendar years as x-values. Instead, enter the x ~Values 0, 5, 10, 15, ,45. Keep in mind thatx = 0 represents January 1 of 1950, x = 5 represents January 1, 1955, and so on. Independent variable x represents the number of years since 1950. Equation without round-off: 3 :4? 251t- 28 12372573 it. “i” I"? g. 233\$ 36 36:; Equation with slope rounded to the nearest tenth and y-intercept rounded to the nearest whole number: For parts b) and c) use the rounded-off model from part a). b) Sketch the regression line on the scatterplot above, and write sentences that interpret the y -intercept and slope of the regression line in context. y —intercept interpretation: “This linear model suggests that...‘in 50 there. ngg no "TV swarms on was are, slope interpretation: “This linear model suggests that... ~§mm MSG "41? mag VikkW‘bﬁ ﬁr oi one elm le graham ‘lm re as ad b3 Gm “Verana a? 2&3 stencicmsa per" c) Predict how many years after 1950 the number of TV stations reaches 1000, and then 2000. For each calculation state whether it represents interpolation or extrapolation. more :1: ﬁrearms“ «gene raritiJX +17? 335 “'2' Zy‘kgx “22'ng 3 Iti-EK x 31%},3 its 31mm (ti-teeters, Knew/i”. 3a,» “7a 3;: ‘t "i?!" Olm‘i‘im’t 3 [NF 5‘ V‘ '0 ex capo rm was; (2.) 5. (2.1—2.2) A refrigerator depreciates overtime. The value is \$850 dollars at age 2 years, and \$450 at age 6 years. a) Write a linear function formula that gives value V v as a function of age A years. What is the independent variable?, V or A? A way! as mod. WK) game-r V... VI “2‘: m( «m Al) awe, J intone? "‘“ 3‘30 :: WEQC) , ml w m ’ \ff‘” 350 a e'lQrEAA-aaipg V” 'QOAc‘l lQSQ ‘0) Sketch the graph (a line segment) from the vertical intercept to the horizontal intercept, and label both intercepts on the sketch. State the domain and range. ' ‘1 m '5‘; ho‘risow’raﬁ. ‘taiewc..eat‘=' mares when Vs: 0 36min“ SAW an A4“ nwtooﬁ M059 as} Analog @aﬂyp. {V‘ ong tosog c) Write sentences that interpret the vertical intercept, horizontal intercept, and slope in the context of value and age. ' . , 1 vertical intercept interpretation: “This linear model suggests that..."HN2, waiftf‘iﬂatf'nfl on S Votive-t was \$2 “250 When it WM new. (Oysters 0‘90 \ ‘ ‘ horizontal intercept interpretation: “This linear model suggests that... (“Grettjagtmi’t or .5 Voila ranches in \O .5 years , . P slope interpretation: “This linear model suggests that...”i’ln€r: i393! calm-“‘5 UQ‘LM‘ﬁ neweaswi cm. aware—3n. \$7” '00 PW year”. 6. (2.2) Hooke’s Law for Springs :1; necessary to stretch a spring from its equilibrium position ngth o is directly proportional mtheile ' “e” stretch) Suppose a force of 24 pounds is required to stretch a particular spring'4 inches. . 94 a) Let F be the force required to stretch this spring x inches, and let k be the constant of proportionality. Find k, and write the formula that give force F as a function of stretch length x. Answers: It: 49 ,so by Hooke’slaw,F= ' Fskx 2r 9:: lee Ken: is b) Find the force necessary to stretch this spring 6 inches from equilibrium. l: :2: (5C; 3% “as 7. (2.5) Consider the function y = —|x — 3] . a) Make a table of values and graph this function. Your table should include as m 3, a few inputs smaller than 3, and a few inputs larger than 3. Then sketch the graph. Label x~intercept and y— intercept as ordered pairs. b) State the domain and range. Over what interval(s) is the function decreasing? domain: (2“‘my"*o°> Clea rue-Mess oven E3froo> . Vﬂaﬁggx‘ {No} 0-1 Net: we is; slim areeuoiaiaig 0';- ﬁrfiﬁegtim} bueiﬂwo’it"‘iﬂ 5- a t” \ooei‘ﬁ o Linear Regression with TI—83, 83+, and 84 Calculators To clear lists and enter my) data: 1. Press Stat, Edit. When necessary, clear data from a list by highlighting the list name at the top, and then press CLEAR followed by the down-arrow key. 2. Enter the numerical values for .1: into I,E , pressing ENTER after each entry. Then press the right— arrow key to move the cursor to L2 and enter the corresponding y—values in the same manner. To obtain a linear regression equation With the x-data in L1 and y-data in L2 , From the home screen, press Stat and arrow to the CALC menu. Arrow down to either LinReg(ax+b) or LinReg(a+bx) and press ENTER. The calculator goes back to the home screen, and “LinReg” appears followed by a ﬂashing cursor. You are being prompted to tell the calculator which lists to use for the x-data and y~data. At the ﬂashing cursor type 2“Cl 1 to indicate L, for the x-data, then the comma key, and ﬁnally 2‘”I 2 to indicate L2 for the y-data. When you press ENTER the calculator gives the a-value and b-value for the equation y = ax + b . To obtain a scatterplot With the x-data in L, and the y—data in L2 , .. 1. press 2nd, Y: to get the STAT PLOTS screen, and press ENTER. Highlight On, press ENTER, ' and arrow to. Type. Highlight the ﬁrst of the six choices (looks like a scatterplot) and press ENTER. For Xlist press 2"", 1 to indicate L1, and 2"“, 2 to indicate L2. For Mark, highlight any of the choices (the larger, box-like mark is recommended.) 2. Press ZOOM, arrow to ZoomStat, and press ENTER. The calculator automatically chooses a window size appropriate for the task. You may press WINDOW to change any of the graph window settings. To graph the regression line on the scatterplot Press Y= , enter the regression formula in one of the Y= locations and press GRAPH. Note: Normal graphing features of the calculator will not work until you deactivate Plot 1 (and any other active Plot windows). To deactivate a Plot window like Plot 1, press Y=, highlight Plot 1, and press ENTER to turn it off. ...
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1105_LW2_solutions_F11 - MAC1105 Lecture Worksheet 2...

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