MATH CONCEPTS CALCULUS
MATH CONCEPTS CALCULUS MATH 131
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This 6 page Class Notes was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Class Notes belongs to MATH 131 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/226047/math-131-texas-a-m-university in Mathematics (M) at Texas A&M University.
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Date Created: 10/21/15
Math 131 Exam 1 quotSample Questions This is a compilation of exam I questions from old exams written by various instructors They cover all of chapter one except for 13 The solutions can be found at the end of the document 1 A city has an annual population growth rate of 2 Assuming exponential growth how many years will it take the population to double to the nearest year a 8 years b 17 years c 23 years d 35 years e none of the above 2 Given the equation P 1816 095 convert this to the form P Poe a P 520 e25 b P 17252 e005 c P 1816e 39 5 d P 1816 amquot e none of the above 3 What is the effective annual yield of an investment paying at a 10 annual rate compounded quarterly a 1038 b 1105 c 1047 d 1052 e none of the above 4 2 2 Simplify the expression W 1nx y l 5 Which formula best represents the relationship shown in the table IX2I22I24I26I28I IfXI 2 I242 288 338 392I a x mx b b 17906062 c 17906063 d fxagtb 6 Use your calculator to nd all intersection points of y 2x and y x3 Round to 3 decimal places Which lnction dominates as x approaches infinity Choose the fuhetroh whreh represents the graph grveh below The penod is a b x 3cos6x7l x x e3srho 3 none ofthe a ova 8 If fr10 and gr1ogrwhatrs gx7 eorhposrtroh offuncuons a 10 logx b x e 1 3 none ofthe above 9 Choose the fuhetroh whreh represents the graph grveh below a x 0 3x3xi2x75 b x 7015x3x722x7 5 e x 70 3x e 3x 2x 5 01 x 9X3 X 22X 5 3 none ofthe above A xrmte eepts are 73 2 and 5 yrmter ptrs 9 The number of bacteria in millions in a bottle of milk a er 1 days is given in the table below da 0 1 2 3 4 of bacteria resent Determine a formula of the form Q Qoek that gives the number of bacteria present Q in millions as a lnction of t days If the milk cannot be safely consumed when the bacteria count is greater than 3 billion per bottle how many days will the bottle of milk be safe to drink Suppose f g and h are functions of x such that one of them is proportional to x one is inversely proportional to x and one is proportional to the square of x Using the table below write f g and h as functions of x and nd the constants of proportionality The pro t lnction for a skateboard company is given by Px x2 70x 125 where x is the price charged by the company for a skateboard a Find the price that will maximize pro ts b For what prices will the company make a pro t What nominal interest rate has an effective annual yield of 5 under continuous compounding Round the percent to 2 places An animal skull still has 20 of the carbon14 that was present when the animal died The halflife of carbon14 is 5730 years Find the approximate age of the skull to the nearest year The depth of water in a tank oscillates once every 6 hours around an average depth of 7 feet If the smallest depth is 55 feet and the largest depth is 85 feet nd a formula for the depth in terms of time measured in hours Assume the water level starts at 55 feet 20 21 22 23 24 A female boll weevil can lay on average 200 eggs source North Carolina Department of Agriculture Suppose for simplicity39s sake that each boll weevil results in 75 boll weevils the following year Let y be the number of boll weevils in a particular eld in 1995 a Suppose there were only 2 boll weevils in a particular eld in 1995 Give an exponential model for y b According to the model how many boll weevils would be in that eld in the year 2000 Your grandparents put aside 10000 in an account which earns 8 interest for your college when you were born a How much would you have in the account in 18 years if interest was compounded monthly b When would you have 40000 in the account if the interest was compounded continuously Describe how the graph of y 2 f x 3 4 di ers from the graph of y fx If gx x2 x nd and simplify gx h gx Determine lnctions f and g such that f g x 63H Do not choose x x or gx x The model y 5 49cos t represents the water level y in feet at Padre Island I hours a er midnight a Find the range of the water level at Padre Island b Find the period of this lnction to nd the amount of time between high tides c How high is the water level at 130pm according to the model The population in country A is 40 million on January 1 1990 and increases by 6 each year therea er The population in country B is 60 million on January 1 1990 and increases by 4 each year therea er How long will it take for the population in country A to surpass the population in country B A local bank is offering a savings account with an annual interest rate of 569 compounded quarterly What should be the annual interest rate of an account whose interest is compounded continuously but which has the same effective annual yield If the population of the world was 2564 billion in 1950 and the annual population growth rate was 185 nd an exponential equation to model the population of the world as a lnction of time since 1950 According to your model during what year will the population rst reach 7 billion 25 Gwen the followmg graphs ndthexr equauons Use the formy x Round to 3 demmal places a Po nts gwen 0 2 and 2 1 Pox s gwen o 8 and 3 0 Points gwen 73 0 1 0 5 0 and 0 e2 5 01 The panode andtheyrmterceptxs 0 3 pwsowwwe wwocw9gtoc 10 11 12 13 14 15 VI 373 2591 and 9940 981970 2 Q 500e0391m about 15 days fx 3000 gx 2x2 hx 025x x a 35 b 183 lt x lt 6817 488 13305 years y 15cos t 7 wherey is depth in feet and t is time in hours Solutions 131 ExamI quotSample Questionsquot HHH 9080 O UI a y 275 b 4746093750 a 4200574 b 173 years stretched by a factor of 2 longer shi ed 3 units right and 4 units up 2xhh2 h 20 2 22 23 24 2 fxe and gx3x 2 a 01 Sy 399 b 12 hours 0 846 feet 2129 years 565 2004 a y 20707r b y JC 32 0 y x3x 12x 5 d y 3 sin8x 3
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