1105_LW2_2.1,2.2,2.5_F11

1105_LW2_2.1,2.2,2.5_F11 - MACllOS Lecture Worksheet 2...

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Unformatted text preview: MACllOS 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. a) Complete this table for Delbert’s total monthly b) _Write an algebraic equation that expresses 1 income on monthly sales of $0, $2000, $4000, $6000, $8000, and $10,000. Monthly Sales, S Total Monthly Income,i $0 - Income in Dollars 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, I or S? From your graph, estimate the monthly sales for which Delbert’s monthly income is $1500. Then use your equation from part a) to find the exact sales amount algebraically. 2000 4000 6000 8000 5-3135 in Donars 10000 12000 Graphic estimate: m $ Algebraic Exact Result: = $ (:1) Write sentences that interpret the slope and vertical intercept of the graph. 2. (2.2) Parts I—IH 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. I. The equation ofline 1 is 1 a)xm—l b)y=—1 c)y=—§x d)_xl=3 e)ym3 II. The slope of line 2 is b) —4 b) 4 -c) undefined (no slope) d) —% e) 0 III. The equation of line 3 is c) yn—éx—Li b) y=m4x~4 c) y%—4x d) ym—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 —I. IV. The slope of any line perpendicular to line 3 is d) —4 b) 4 c) undefined (no slope) d) Hm e) — 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 pounds. Let y = the boy’s weight (in pounds) at age It months a) Write a formula for a linear function that gives this boy’s weight as a function of his age. Answer: y = b) Complete this sentence: The equation in part a) suggests that this boy weighed pounds at birth, and his weight is at an average rate of ( increasing or decreasing '2') (numerical answer) (correct units for 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. . 5' ._ Number of U.S. Onwhiz TV Stations E 13 15 29 25 BB 35 4B 45 EB 55 .233 Time (39315 from 1950: a) Use the calculator to carry 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 that x = 0 represents January 1 of 1950, x = 5 represents January 1, 1955, and so on. Independent variable x represents the number of ye ars since 1950. Equation without round-off: 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). 1)) 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... slope interpretation: “This linear model suggests that... 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. 5. (2.1-2.2) A refrigerator depreciates over time. 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?, VorA? 1200 V: b) 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. 0) Write sentences that interpret the vertical intercept, horizontal intercept, and slope in the context of value and age. vertical intercept interpretation: “This linear model suggests that... horizontal intercept interpretation: “This linear model suggests that... SIOpe interpretation: “This linear model suggests that. . . 6. (2.2) Hooke’s Law for Springs The force necessary to stretch a spring from its equilibrium position is directly proportional to the length of the stretch. Suppose a force 01°24 pounds is required to stretch a particular spring'4 inches. . a) Let F be the force required to stretch this spring x inches, and let k be the constant of proportionality. Find it, and write the formula that give force F as a function of stretch length x. Answers: If = , so by Hooke’s law, F = b) Find the force necessary to stretch this spring 6 inches from equilibrium. 7. (2.5) Consider the function y = Mix-31. a) Make a table of values and graph this function. Your table should include x = 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? Linear Regression with TI-83, 83+, and 84 Calculators To clear lists and enter £35,331 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 x into L1 , 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 L] and y-dat'a 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 2nd 1 to indicate L, for the X—data, then the comma key, and finally 2"" 2 to indicate L, 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 L1 and the y—data in L2 , l. 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 (iooks iike a scatterplot) and press ENTER. For Xlist press 2‘”, 1 to indicate L, , 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 scatteiplot 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_2.1,2.2,2.5_F11 - MACllOS Lecture Worksheet 2...

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