Paper Help  The halflife of the radioactive element krypton
The halflife of the radioactive element krypton

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The halflife of the radioactive element krypton Question 1 of 402.5 PointsThe halflife of the radioactive element krypton91 is 10 seconds. If 16 grams of krypton91 are initiallypresent, how many grams are present after 10 seconds? 20 seconds?A. 10 grams after 10 seconds; 6 grams after 20 secondsB. 12 grams after 10 seconds; 7 grams after 20 secondsC. 4 grams after 10 seconds; 1 gram after 20 secondsD. 8 grams after 10 seconds; 4 grams after 20 seconds Question 2 of 402.5 PointsApproximate the following using a calculator; round your answer to three decimal places.3?5A. .765B. 14297C. 11.494D. 11.665Question 3 of 402.5 PointsWrite the following equation in its equivalent exponential form.5 = logb 32A. b5 = 32B. y5 = 32C. Blog5 = 32D. Logb = 32Question 4 of 402.5 PointsWrite the following equation in its equivalent exponential form. 4 = log2 16A. 2 log4 = 16B. 22 = 4C. 44 = 256D. 24 = 16 Question 5 of 402.5 PointsWrite the following equation in its equivalent exponential form.log6 216 = yA. 6y = 216B. 6x = 216C. 6logy = 224D. 6xy = 232Question 6 of 402.5 PointsSolve the following exponential equation by expressing each side as a power of the same base and thenequating exponents.31x = 1/27A. {2}B. {7}C. {4}D. {3}Question 7 of 402.5 PointsUse properties of logarithms to expand the following logarithmic expression as much as possible. Logb (?xy3 / z3)A. 1/2 logb x – 6 logb y + 3 logb z B. 1/2 logb x – 9 logb y – 3 logb zC. 1/2 logb x + 3 logb y + 6 logb zD. 1/2 logb x + 3 logb y – 3 logb zQuestion 8 of 402.5 PointsEvaluate the following expression without using a calculator.Log7 ?7A. 1/4B. 3/5C. 1/2D. 2/7Question 9 of 402.5 PointsFind the domain of following logarithmic function.f(x) = log (2 – x)A. (?, 4)B. (?, 12)C. (?, 2)D. (?, 3)Question 10 of 402.5 PointsUse the exponential growth model, A = A0ekt, to show that the time it takes a population to double (togrow from A0 to 2A0 ) is given by t = ln 2/k.A. A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = tB. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = tC. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = tD. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toeQuestion 11 of 402.5 Points Find the domain of following logarithmic function. f(x) = log5 (x + 4)A. (4, ?)B. (5, ?)C. (7, ?)D. (9, ?)Question 12 of 402.5 PointsWrite the following equation in its equivalent logarithmic form.24 = 1/16A. Log4 1/16 = 64B. Log2 1/24 = 4C. Log2 1/16 = 4D. Log4 1/16 = 54Question 13 of 402.5 PointsEvaluate the following expression without using a calculator.8log8 19A. 17B. 38C. 24D. 19Question 14 of 402.5 PointsWrite the following equation in its equivalent logarithmic form. 3?8 = 2A. Log2 3 = 1/8 B. Log8 2 = 1/3C. Log2 8 = 1/2D. Log3 2 = 1/8 Question 15 of 402.5 PointsYou have $10,000 to invest. One bank pays 5% interest compounded quarterly and a second bank pays4.5% interest compounded monthly. Use the formula for compound interest to write a function for thebalance in each bank at any time t.A. A = 20,000(1 + (0.06/4))4t; A = 10,000(1 + (0.044/14))12tB. A = 15,000(1 + (0.07/4))4t; A = 10,000(1 + (0.025/12))12tC. A = 10,000(1 + (0.05/4))4t; A = 10,000(1 + (0.045/12))12tD. A = 25,000(1 + (0.05/4))4t; A = 10,000(1 + (0.032/14))12t Question 16 of 402.5 PointsUse properties of logarithms to expand the following logarithmic expression as much as possible.logb (x2 y) / z2A. 2 logb x + logb y – 2 logb zB. 4 logb x – logb y – 2 logb zC. 2 logb x + 2 logb y + 2 logb zD. logb x – logb y + 2 logb zQuestion 17 of 402.5 PointsUse properties of logarithms to expand the following logarithmic expression as much as possible. logb (x2y)A. 2 logy x + logx yB. 2 logb x + logb yC. logx – logb y D. logb x â logx y Question 18 of 402.5 PointsUse properties of logarithms to condense the following logarithmic expression. Write the expression as asingle logarithm whose coefficient is 1.log x + 3 log yA. log (xy)B. log (xy3)C. log (xy2)D. logy (xy)3Question 19 of 402.5 PointsSolve the following exponential equation by expressing each side as a power of the same base and thenequating exponents.ex+1 = 1/eA. {3}B. {2}C. {4}D. {12}Question 20 of 402.5 PointsConsider the model for exponential growth or decay given by A = A0ekt. If k __________, the functionmodels the amount, or size, of a growing entity. If k __________, the function models the amount, orsize, of a decaying entity.A. > 0; < 0B. = 0; ? 0C. ? 0; < 0D. < 0; ? 0Question 21 of 40 2.5 PointsLet x represent one number and let y represent the other number. Use the given conditions to write asystem of equations. Solve the system and find the numbers.The sum of two numbers is 7. If one number is subtracted from the other, their difference is 1. Find thenumbers.A. x + y = 7; x – y = 1; 3 and 4B. x + y = 7; x – y = 1; 5 and 6C. x + y = 7; x – y = 1; 3 and 6D. x + y = 7; x – y = 1; 2 and 3Question 22 of 402.5 PointsWrite the partial fraction decomposition for the following rational expression.x + 4/x2(x + 4)A. 1/3x + 1/x2 – x + 5/4(x2 + 4)B. 1/5x + 1/x2 – x + 4/4(x2 + 6)C. 1/4x + 1/x2 – x + 4/4(x2 + 4)D. 1/3x + 1/x2 – x + 3/4(x2 + 5)Question 23 of 402.5 PointsWrite the form of the partial fraction decomposition of the rational expression.7x – 4/x2 – x – 12A. 24/7(x – 2) + 26/7(x + 5)B. 14/7(x – 3) + 20/7(x2 + 3)C. 24/7(x – 4) + 25/7(x + 3)D. 22/8(x – 2) + 25/6(x + 4)Question 24 of 402.5 PointsWrite the partial fraction decomposition for the following rational expression. x2 â 6x + 3/(x â 2)3 A. 1/x â 4 â 2/(x â 2)2 â 6/(x â 2)B. 1/x â 2 â 4/(x â 2)2 â 5/(x â 1)3C. 1/x â 3 â 2/(x â 3)2 â 5/(x â 2)D. 1/x â 2 â 2/(x â 2)2 â 5/(x â 2)3Question 25 of 402.5 PointsSolve the following system.x+y+z=63x + 4y – 7z = 12x – y + 3z = 5A. {(1, 3, 2)}B. {(1, 4, 5)}C. {(1, 2, 1)}D. {(1, 5, 7)}Question 26 of 402.5 PointsSolve each equation by the substitution method.x2 – 4y2 = 73×2 + y2 = 31A. {(2, 2), (3, 2), (1, 2), (4, 2)}B. {(7, 2), (3, 2), (4, 2), (3, 1)}C. {(4, 2), (3, 2), (5, 2), (2, 2)}D. {(3, 2), (3, 2), (3, 2), (3, 2)}Question 27 of 402.5 PointsSolve the following system. 2x + 4y + 3z = 2x + 2y – z = 0 4x + y – z = 6A. {(3, 2, 6)}B. {(4, 8, 3)}C. {(3, 1, 5)}D. {(1, 4, 1)}Question 28 of 402.5 PointsWrite the partial fraction decomposition for the following rational expression.6x – 11/(x – 1)2A. 6/x – 1 – 5/(x – 1)2B. 5/x – 1 – 4/(x – 1)2C. 2/x – 1 – 7/(x – 1)D. 4/x – 1 – 3/(x – 1)Question 29 of 402.5 PointsPerform the long division and write the partial fraction decomposition of the remainder term.x5 + 2/x2 – 1A. x2 + x – 1/2(x + 1) + 4/2(x – 1)B. x3 + x – 1/2(x + 1) + 3/2(x – 1)C. x3 + x – 1/6(x – 2) + 3/2(x + 1)D. x2 + x – 1/2(x + 1) + 4/2(x – 1) Question 30 of 402.5 PointsSolve the following system by the addition method. {4x + 3y = 15{2x â 5y = 1A. {(4, 0)} B. {(2, 1)}C. {(6, 1)}D. {(3, 1)} Question 31 of 402.5 PointsWrite the partial fraction decomposition for the following rational expression.1/x2 â c2 (c ? 0)A. 1/4c/x – c – 1/2c/x + cB. 1/2c/x – c – 1/2c/x + cC. 1/3c/x – c – 1/2c/x + cD. 1/2c/x – c – 1/3c/x + c Question 32 of 402.5 PointsSolve each equation by either substitution or addition method.x2 + 4y2 = 20x + 2y = 6A. {(5, 2), (4, 1)}B. {(4, 2), (3, 1)}C. {(2, 2), (4, 1)}D. {(6, 2), (7, 1)} Question 33 of 402.5 PointsSolve each equation by the addition method. x2 + y2 = 25(x – 8)2 + y2 = 41 A. {(3, 5), (3, 2)}B. {(3, 4), (3, 4)}C. {(2, 4), (1, 4)}D. {(3, 6), (3, 7)}Question 34 of 402.5 PointsWrite the partial fraction decomposition for the following rational expression.ax +b/(x â c)2 (c ? 0)A. a/a â c +ac + b/(x â c)2B. a/b â c +ac + b/(x â c)C. a/a â b +ac + c/(x â c)2D. a/a â b +ac + b/(x â c)Question 35 of 402.5 PointsSolve each equation by the substitution method. x+y=1×2 + xy â y2 = 5A. {(4, 3), (1, 2)}B. {(2, 3), (1, 6)}C. {(4, 3), (1, 3)}D. {(2, 3), (1, 2)} Question 36 of 402.5 PointsMany elevators have a capacity of 2000 pounds. If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when xchildren and y adults will cause the elevator to be overloaded. A. 50x + 150y > 2000B. 100x + 150y > 1000C. 70x + 250y > 2000D. 55x + 150y > 3000 Question 37 of 402.5 PointsWrite the form of the partial fraction decomposition of the rational expression.5×2 – 6x + 7/(x – 1)(x2 + 1)A. A/x – 2 + Bx2 + C/x2 + 3B. A/x – 4 + Bx + C/x2 + 1C. A/x – 3 + Bx + C/x2 + 1D. A/x – 1 + Bx + C/x2 + 1Question 38 of 402.5 PointsSolve the following system by the substitution method. {x + y = 4{y = 3xA. {(1, 4)}B. {(3, 3)}C. {(1, 3)}D. {(6, 1)}Question 39 of 402.5 PointsWrite the partial fraction decomposition for the following rational expression. 4/2×2 – 5x â 3A. 4/6(x – 2) – 8/7(4x + 1) B. 4/7(x – 3) – 8/7(2x + 1)C. 4/7(x – 2) – 8/7(3x + 1)D. 4/6(x – 2) – 8/7(3x + 1)Question 40 of 402.5 PointsOn your next vacation, you will divide lodging between large resorts and small inns. Let x represent thenumber of nights spent in large resorts. Let y represent the number of nights spent in small inns. Write a system of inequalities that models the following conditions: You want to stay at least 5 nights. At least one night should be spent at a large resort. Large resortsaverage $200 per night and small inns average $100 per night. Your budget permits no more than $700for lodging.A.y?1x+y?5x?1300x + 200y ? 700B.y?0x+y?3x?0200x + 200y ? 700C.y?1x+y?4x?2500x + 100y ? 700D.y?0 x+y?5x?1200x + 100y ? 700