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# COLLEGE ALGEBRA MATH 121G

NMSU

GPA 3.93

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This 0 page Class Notes was uploaded by Florence Blanda on Sunday November 1, 2015. The Class Notes belongs to MATH 121G at New Mexico State University taught by Abby Train in Fall. Since its upload, it has received 78 views. For similar materials see /class/233196/math-121g-new-mexico-state-university in Mathematics (M) at New Mexico State University.

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Date Created: 11/01/15

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Viv Sc3t M 53L7L11 T3xdm 3amp6 mfgwe 4m wkmw mi SW5 art 7 1 bi Ch 5392 LL 1 G T 5Q5 Q Log Hme T 50 00 QESSLE 50 490 UKUJM b 5DQU E 5 1 D 150 M 3 164 500 500 1 H T 0 Tim quot2 90 was m btgo IO gt haw Q qult lgt 2050 mug 23 EH 500 Q05 H T so 3lt Egg D 9 3 500 m BH39O T 310 g B LJO 986 pm t Q 3 IN 80 ELOO i8t 5 E 9 184c9mq o T18 C A QM 3 50 8 E Math 121 Fall 2010 nal Exam Review PLEASE NOTE You must show work on exam to receive credit 1 D b 4 LI 0 1 Find an equation of the linear function which a passes through the points 2 3 and 41 b is vertical and passes through 1 0 is horizontal and passes through 45 is perpendicular to 4x y 7 and passes through 13 Q A small appliance manufacturer finds that it costs 9000 to produce 1000 toaster ovens a week and 12000 to produce 1500 in a week a Assuming the relationship is linear express the cost C as a function of the number of toaster ovens produced x b Find the vertical intercept What does it represent in the context of this problem c Explain the slope in the context of this problem Solve the system of inequalities 5y 3x S 10 and 5y x 2 10 by graphing Make sure to label the vertical intercepts and the intersection point Clearly show all work Solve the following systems of two linear equations algebraically either by substitution or elimination 4x3y 3 5x 2y 95 x 3 y 2 2xy1 y The tax code in a particular state requires residents to pay 15 income tax on the first 30000 they earn and 25 on any income above that level Find a piecewise linear function that gives the amount of tax owed as a function of income Graph the function labeling the axes appropriately A large wholesale nursery sells shrubs to retail stores Their cost Cx 15x12 000 and revenue Rx 18x where x is the number of shrubs sold What is the breakeven point Use the conversion chart in the back of your book to solve the following conversion problems a How many uid ounces are there in a 2 liter bottle of coke b If you make 45000 per year what is your salary in dollarshour assuming a 40 hour work week and 52 weeks per year 00 D H H H H 3 Simplify using the properties of exponents Write your answer using only positive exponents a zxsyrzf 1 3 2 b r r r13 Use the properties of logarithms to write as a single logarithm a 4logx7logy 810gz b lnx21ny 4 Use properties of logarithms to expand the following Mil Solve the following equations for x a log6x l b 563x i 10 C erx2 5 d ln2x 1 100 e 3lnx 1 7 Please find the domain and range of each function below It will be helpful if you sketch a rough graph a fx J2x 3 b gx 5090X c hx 13 3x Hint Find Vertex A waste water treatment facility is treating water contaminated with 28 micrograms of pollutant per liter The waste water is treated multiple times and each treatment removes 20 of the current pollutants a Find a model which represents the amount of pollutant Pn in the water after n treatments Make a table of values with the number of treatments ranging from n 0 to n 13 Based on this table of values estimate the half life that is how many times does the water need to be treated so that half of the pollutants are eliminated When does the amount of contaminants per liter become less than 2 micrograms c Algebraically solve the problems posed in part b above 5 14 A family of 100 termites invades a house with the population growing exponentially If H LII H 0 H 00 the colony doubles every three weeks find a model for the number of termites in the house as a function of time t in weeks How many termites will there be after 1 year At what time will there be a billion termites nt Use the interest formulas A P 1LJ and A P6 to solve the following interest n problems a Suppose you invest 7500 into an investment account bearing a nominal rate of 72 interest compounded quarterly monthly What would these accounts be worth in 40 years What are the effective rates of interest on these accounts b How long would it take an investment to double if it bears 54 interest compounded continuously What would be the effective rate on this account A metal ball is dropped from the top of the 1450 foot high Sears Tower in Chicago If the distance the ball falls is directly proportional to the square of the time it is allowed to fall and after 1 second the ball falls 16 feet find the formula d t for the distance the ball has fallen after t seconds At what time will the ball hit the ground The speed s of the ball is given by the formula st 32t How fast is the ball traveling when it hits the ground The weight of a body is inversely proportional to the square of the distance from the body to the center of the Earth Assume the Earth has a radius of 4000 miles a How much will a person who weights 150 lbs on the surface of the earth weigh 2000 miles above the earth b At what distance from the center of the Earth will a body weight 10 of its weight on the surface of the Earth Follow the instructions for the following quadratics g x x2 2x hx 2x2 4x 4 a Complete the square and put the function in vertex form Verify your answer by using the formula for the axis of symmetry x 2 a b Use the vertex form to solve for the horizontal intercepts Verify your answer using the quadratic formula c Graph the function labeling the vertex axis of symmetry and the horizontal intercepts State the focal length and find the coordinates of the focus Q 19 An expresso stand finds that its weekly profit is a function of the price x it charges per cup If xis the price of a cup of coffee in dollars then the weekly profit is given by the function Px 2900x2 7250x 2900 dollars a Use the formula x g b to find the axis of symmetry of the profit function a b What price per cup would maximize weekly profit and what would be the maximum weekly profit Use the quadratic formula to find the horizontal intercepts of the profit function Use all of the above information to sketch a graph of the profit function so 20 Follow the directions below a If fx 2 and gx ex find fgx b If fx2xl and gxlnxfind gfx 0 where t is in seconds 21 The voltage V across a charged capacitor is given by Vt Se a What is the voltage after 3 seconds b Find the inverse function tV Hint All you have to do is take V 56 and solve for t c Use your inverse function to answer the question When will the voltage be 1 22 Solve for the variable listed below a T 5050010g1 for D b B 4806quot97s for t

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