1. Exponential and Logarithmic functions

    A certain material decays at a rate of 1.9% per year. The sample is 260 grams. How much will be left in 11 years? How long will it take to have only a 100g sample left?
  2. calculus

    The rate at which an amount of a radioactive substance decays is modeled by the differential equation dA/dt = kA, where A is the mass in grams, t is the time in years, and k is a constant. Answer the following. a) If a 100-gram sample of the radioactive substance decays to 95 ...
  3. algebra

    Suppose a sample of Cesium-137 with initial mass of 200 grams decays to a mass of 160 grams voer the course of 10 years. Find the half-life of Cesium-137 (Round to the nearest year) How much Cesium-137 is left in the sample after 60 years? Round to the nearest tenth of a gram.
  4. AP Calculus

    An Initial amount of 100 grams of Thorium-234 decays according to the model: dP/dt=-0.02828P (where t is measured in years). a) Find the equation for the amount of Thorium left after t years. b) Determine the half-life of this radioactive isotope c) How long will it take for ...
  5. Physics/Math

    A 25.0 gram piece of charcoal is found in some ruins of an ancient city. The sample shows a 14C activity, R, of 250 decays/min. How long (in years) has the tree this charcoal came from been dead? I think I have the use the equation: R=lamda*No*e^(-lamda*t) but I am not sure ...
  6. Calculus

    A certain radioactive material decays exponetially. The percent, P, of the material left after t years is given by P(t)= 100(1.2)^-t a)Determine the half life of the substance
  7. Pre Calculus

    If a 25 mg sample of radioactive material decays to 18.4 mg in 5 years, how long will it take the sample to decay to 20.5 mg?
  8. math

    Suppose strontium-90 decays at a rate of 2 percent per year. (a) Write the fraction P of strontium remaining, as function of t, measured in years. (Assume that at time t=0 there is 100 % remaining.) Answer: P(t)=(.98)^t (b) Estimate the half-life of strontium. (c) If presently...
  9. College algebra

    Sample of 500gms radioactive substance decays according to the function A(t)-500-0.044t where t is the time in years. How much of the substance will be left in the sample after 20 years?round to the nearest whole gram
  10. College Algebra

    The half-life of a radioactive material is about 34.6 years. How much of a 1-gram sample of the material is left after 30 years?
  11. science

    As redioactive material decays and the percentage of new material in the original sample increases, does the age of the sample substance increase, decrease, or remain the same?
  12. algebra

    A radioactive substance decays according to the formula A=A0e^kt where A0 is the initial amount of substance (in grams) A is the amount of substance(in grams) after t years k is a constant The half-life of the substance is 10 years.If we begin with 20g of the substance,how ...
  13. Math

    A radioactive material has a half life of 500 years. A) Given 20 grams of this material, how much will remain after 1,000 years? B) Given 100 grams of this material, how much will remain after 750 years? Thank you to whom ever can help me :)
  14. Math

    Suppose strontium-90 decays at a rate of 2 percent per year. (a) Write the fraction P of strontium remaining, as function of t, measured in years. (Assume that at time t=0 there is 100 % remaining.) Answer: P(t) = (b) Estimate the half-life of strontium. Answer: Hint: Use your...
  15. calculus

    Suppose strontium-90 decays at a rate of 2 percent per year. (a) Write the fraction P of strontium remaining, as function of t, measured in years. (Assume that at time t=0 there is 100 % remaining.) Answer: P(t) = (b) Estimate the half-life of strontium. Answer: Hint: Use your...
  16. NEED HELP WITH CALC

    Suppose strontium-90 decays at a rate of 2 percent per year. (a) Write the fraction P of strontium remaining, as function of t, measured in years. (Assume that at time t=0 there is 100 % remaining.) Answer: P(t) = (b) Estimate the half-life of strontium. Answer: Hint: Use your...
  17. Chemistry

    It took 109.8 years for a 300.0 mg sample of an unknown radioactive material to completely disintegrate. Calculate the mass of the element (in grams/mole) assuming that the disintegrations per second are constant over the life-time of the sample, and the sample is labeled 100....
  18. Physics

    A gram of living plant material with Carbon-14 , decays at a rate of about 16 disintegrations per minute. When the plant dies, the Carbon-14 decays, with a half-life of 5600 years. A gram of the dead plant is found to decay at about 1 disintegration per minute. Calculate the ...
  19. Math - Exponential Decay

    Radium decays exponentially. Its half-life is 1,690 years. How long will it take for a 50-gram sample of radium to be reduced to 5 grams? 1/2P = Pe^(-1690k) (ln1/2)/(-1690) = k 4 x 10^-4 = k 5 = 50e^-kt ln0.1 = -kt ln0.1/-k = t 5,630 years = t ...but textbook answer is 5,614 ...
  20. precalc

    I am really struggling with a bunch of problems. Any help with any of the following would be greatly appreciated. Thanks 1. ln e^(ln x) - ln(x - 3) = ln 8 2.3e^(6x - 2) = 18 The word problems, especially, are killing me. 3. In the formula A = Iekt, A is the amount of ...
  21. science

    A substance has a half-life of 10,000 years and an initial mass of 1,000 grams. How many years will pass before only 250 grams of the substance's parent material is left?
  22. FINANCE 200

    You receive $5000 three years from now. The discount rate is 8 percent. What is the value of your investment two years from now? (Multiply 5000 by .926 (one year discount rate at 8%) Will it be worth $9,260?
  23. algebra 2

    In the formula A(t) = A0ekt, A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 72% of the carbon-14 it ...
  24. Algebra please check my answers

    1) The linear function f(x) contains the points (-10, -29) and (-2, 83). If g(x) = 25x - 50, which statement is true? A. The functions f(x) and g(x) both have positive slopes. <<< B. The functions f(x) and g(x) both have negative slopes. C. The function f(x) has a ...
  25. Science

    If 15% of the radioactive material decays in 5 days, what would be the percentage of amount of original material left after 25 days?
  26. Algebra-Problems

    Please help with my word problems? Solve the problem. The rabbit population in a forest area grows at the rate of 6% monthly. If there are 260 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. Use y=260(2.7)^0.06t...
  27. Pre Calculus

    Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 69 grams, how much will remain after 75 years? a. 1.5848 grams b. 61.5289 grams c. 0.0000 grams d. 1.0426 grams e. 17.2500 grams
  28. Environmental Science 11th grade

    If half of a quantity of radioactive material decays in 10 years, in another 10 years?
  29. Word Problems-Math

    Please help with my word problems? Solve the problem. The rabbit population in a forest area grows at the rate of 6% monthly. If there are 260 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. Use y=260(2.7)^0.06t...
  30. Algebra I

    A sample of radioactive material weighing 45 grams has a decay rate of 4.25% each day. The equation y = 45(2.7)–0.0425t can be used to find the amount of material that still remains, where t is the number of days that have passed. Approximately what is the amount of material...
  31. Physics

    If a sample of a radioactive isotope has a half-life of 5 year(s), how much of the original sample will be left at the end of the second year? How much will be left at the end of the third year of thr original sample? How much will be left at the end of the fourth year of the ...
  32. fin

    The following tabulation gives earnings per share figures for the Foust Company during the preceding 10 years. The firm’s common stock, 7.8 million shares outstanding, is now (1/1/03) selling for $65 per share, and the expected dividend at the end of the current year (2003) ...
  33. Physics!

    The activity of a sample of 35(upper#) 16(lower#)Sulfer (T 1/2= 7.55x10^6 s) is 2.51x10^5 decays per second. WHat is the mass of the sample? m= in grams PLease help me out...Thank you! :)
  34. Physics

    The activity of a sample of 35(upper#) 16(lower#)Sulfer (T 1/2= 7.55x10^6 s) is 2.51x10^5 decays per second. WHat is the mass of the sample? m= in grams PLease help me out...Thank you! :)
  35. Physics Plz help me

    The activity of a sample of 35(upper#) 16(lower#)Sulfer (T 1/2= 7.55x10^6 s) is 2.51x10^5 decays per second. WHat is the mass of the sample? m= in grams PLease help me out...Thank you! :)
  36. Physics Plz help me

    The activity of a sample of 35(upper#) 16(lower#)Sulfer (T 1/2= 7.55x10^6 s) is 2.51x10^5 decays per second. WHat is the mass of the sample? m= in grams PLease help me out...Thank you! :)
  37. Math

    Suppose you wnat to purchase a house for 650,000. Hoe much of the loan would be left after 10 years if the interest rate was 3.8 % and it was a thirty year mortgage? And if you made the montly payments for ten years, and then increase your payment to 4000 per year, how many ...
  38. Physical Science

    A gram of radioactive material has a half-life of one year. After four years how much radioactive material will be left...0g, 1/2g, or 1/4g? None of the above. The answer one-half to the fourth power.
  39. Chemistry - Isotopes

    The isotope caesium 137 has a half life of 30 years. How long will it take for the amount of this isotope in a sample of caesium to decay to one sixteenth of its original amount? Please can someone explain how I can calculate this from the quantities that have been stated? ...
  40. chem

    the following procedure may be used to determine the density of a granular material. A sample of a granular material weighing 4.35 grams is placed in a 15 mL flask and then completely filled with benzene (liquid) the density of which is .879g/cc. The granular material and ...
  41. calculating annuity

    IF a company will generate 80,000 in annual revenue each year for the next eight years and the interest rate is 8.2% what is the present value of the savings? An EXCEL spreadsheet will be helpful for these types of calculations. Let S1 be savings in year 1, S2 in year 2, and ...
  42. Pre Calculus

    Exponential growth and decay find the half life of a radioactive substance if 220 grams of the substance decays to 200 grams in 4 years?
  43. Epidemiology

    Age (Years) Influenza / Pneumonia Deaths (Di) 2007-2011 Population (Pi) from 2007-2011 (2009 used as mid-year) <1 year 7 53,267 1-4 years 4 207,832 5-14 years 5 468,548 15-24 years 14 447,580 25-34 years 27 440,646 35-44 years 40 325,022 45-54 years 92 305,929 55-64 years ...
  44. Science

    A material has 32 atoms in all; 24 decayed and the rest undecayed. If the half-life of the radioactive material is 1000 years, what is the age of the material? a. 1000 years b. 2000 years c. 3000 years d. 4000 years
  45. algebra

    Julie has 250 grams of a radioactive substance. The substance decays every hour. How long will it take until she has 20 grams of the substance left?
  46. Math

    How do I solve this if there is no equation to this 1. The population of the bacteria in a Petri dish increases by a factor of 10 every 10 hour. If there are initally 20 bacteria in the dish, how long will it take before the population increases to 60,000 to the nearest tenth ...
  47. Pre-Calculus

    It is well known that superman can withstand as much as 3 grams of Green Kryptonite indefinitely. However, exposure to more than 3 grams for more than 13 hours is fatal. Assume that Kryptonite decays at an hourly rate of 5.35% If superman is trapped in a room with 6 grams of ...
  48. Calculus

    Suppose strontium-90 decays at a rate of 2 percent per year. (a) Write the fraction P of strontium remaining, as function of t, measured in years. (Assume that at time t=0 there is 100 % remaining.) Answer: P(t)=?
  49. Science/Chemistry

    22Na has a half-life of 951 days. How many grams of a 1.00 kg sample would be left after 4 years?
  50. Physics Help Please

    archaeologist digging at the site of an ancient settlement discover the remains of a wooden structure. carbon 14 dating of the wood from the structure finds a decay rate of 180 decays/min. Knowing that the decay rate for living wood is 600 decays/min and the decay constant for...
  51. chemistry

    Calculate the residence time of sodium in millions of years if the total amount of sodium in the oceans is 1.5 x 10 to the 22 grams, and is supplied to the ocean at a rate of 2.2 x 10 to the 14 grams per year.
  52. Algebra 1

    The function A = A0e-0.01386x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 500 pounds of the material are initially put into the vault, how many pounds ...
  53. economics

    Tom plans to gamble each year for the next 20 years, starting at at the end of year 1. If he loses 4.47 dollars in odd years (i.e., years 1, 3, 5, etc) and wins 7.46 dollars in even years (i.e., years 2,4, 6 etc), what will be Tom's (internal) rate of return per year from ...
  54. precalculus

    The function A=A0e^(-0.0099x) models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 600 pounds of the material are initially put into the vault, how many pounds ...
  55. Physics Help Please! Decay Questions

    archaeologist digging at the site of an ancient settlement discover the remains of a wooden structure. carbon 14 dating of the wood from the structure finds a decay rate of 180 decays/min. Knowing that the decay rate for living wood is 600 decays/min and the decay constant for...
  56. Pre Calculus 1

    thirty percent of a radioactive substance decays in four years. assuming the decay is exponential, find the half life of the substance. the beginning of 1975 the population of a country was 40 million and growing at a rate of 3% per year. Assume that the growth is exponential...
  57. finance

    Barbara wants to save money to meet 2 objectives: i. She would like to be able to retire 25 years from now and have a pension for 15 years after that.She would like to get the first annual payment on the pension 26 years from now, she would like it to be $30,000 and she would ...
  58. algebra

    1) how many billions of years will it take 1000 grams of uranium-238 to decay to just 125 grams? 2) a researcher had 37.5 g left from a 600 g sample of sulfer-35. how many half-lives passed during that time? 3) look at problem 2. how many days passed during that time?
  59. Physics: Fluids

    A sample of an unknown material weighs 260 N in air and 175 N when immersed in alcohol of specific gravity 0.700.
  60. Finance

    We are considering the introduction of a new product. Currently we are in the 34% tax bracket with a 15% discount rate. This project is expected to last five years and then, because this is somewhat of a fad project, it will be terminated. The following information describes ...
  61. math

    Brenda earns $14,260 per year. paid 24 times a year with 1 exemption. If $19.63 in taxes is withheld from each check at what rate is she taxed
  62. science

    If a radioactive isotope has a half life of 10 years and you start with 100 grams what is the fraction left, percentage left, and amount of original in grams I would like for you to explain how to do it not tell me the answer that's the question
  63. College Math

    In a suburb, housing costs have been increasing at 5.2% per year compounded annually for the past 8 years. A house worth $260,000 now would have had what value 8 years ago?
  64. Math

    You invest $7,000 in a two-year CD. At the end of the 2 years, you receive $8,331.97. Assume you left the first year' s interest in the account, what was your yearly interest rate?
  65. Algebra

    Jane agrees to buy a car for a down payment of $4000 and payments of $260 per month for 9 years. If the interest rate is 9% per year, compounded monthly, what is the actual purchase price of her car? (Round your answer to the nearest cent.)
  66. Help meee

    Answer from spreadsheet Answer from hand calculation Problem #1: Find the total amount if you deposit $500 at a rate of 5% for two years using simple interest. Year 1 Year 2 Problem #2: Find the total amount if you deposit $300 at a rate of 6% for three years using simple ...
  67. math

    Brenda Luai earns $14,260 per year. She is paid 24 times per year and claims 1 exemption. If $19.63 in taxes is withheld from each paycheck, at what rate is she taxed?
  68. Math

    Please Help!!!! I do not understand and if someone could help that would be great! Thanks !! Problem #1: Find the total amount if you deposit $500 at a rate of 5% for two years using simple interest. Year 1 Year 2 Problem #2: Find the total amount if you deposit $300 at a rate...
  69. FIN200- FV, PV and Annuity Due CP

    I just want to know if anyone can help me in determining if I am on track with this assignment and if anyone can point out where I am wrong and how I need to fix it. I have already completed this assignment on my own and need someone to review it. Thank You Here is the ...
  70. chemistry

    Please help me through this problem... A 0.5117 gram fertilizer containing phsphorus was oven dried. The weight of the dried sample is 0.4998 grams. However, 10% moisture is still retained in the sample. Calculate the moisture content in the sample in as received and dry basis...
  71. math check

    Brenda Luai earns $14,260 per year. She is paid 24 times per year and claims 1 exemption. If $19.63 in taxes is withheld from each paycheck, at what rate is she taxed?
  72. math algebra

    The amount A, of 70 grams of a certain radioactive material remaining after t years can be found by the equation A=70(0.62)^t. When will 10 grams remain?
  73. pre calc

    A 50 gram sample of radioactive strontium will decay to 32 grams in 18 years. a. Find an equation that will model how much of our sample M will remain after t years.
  74. Fin- Management

    David purchased a $100,000 participating whole life policy. The annual premium is $2,280. Projected dividends for the first 20 years are $15,624. The cash value after 20 years will be $35,260. If the premiums were invested at 5 percent for 20 years, the premiums would grow to...
  75. discrete math

    You have borrowed $8000 from the bank. Suppose you want to repay a fixed amount of money for each of the following n years (except possibly the last year), and the annual interest rate r does not change in these n years. For example, if r = 10% and you repay $4000 each year, ...
  76. math: pre-calculus

    You have 5 grams of carbon-14; whose half-life is 5730 years. a)Write the rule of the function that gives the amount of carbon-14 remaining after x years. b)How much carbon-14 will be left after 4,000 years? c)When will there be just 1 gram left?
  77. FINANCE

    8. Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: 1R1 = 5 percent, E(2r1) = 6 percent, E(3r1) = 7.5 percent E(4r1) = 6.85 percent
  78. accounting

    An amortizing bond is a bond which pays the principal not at its maturity, but prior to its maturity, according to some schedule, typically (but not necessarily) in equal amounts. In particular, consider a floating-rate amortizing bond, which pays 25% of its principal amount ...
  79. finance

    You note the following yield curve in The Wall Street Journal. According to the unbiased expectations theory, what is the 1-year forward rate for the period beginning one year from today, 2f1? (Round your answer to 2 decimal places.) Maturity Yield One day 2.50% One year 6.00 ...
  80. math - interest rates

    Car loan: 5-yr annual-payment loan with interest rate of 6% per year. Annual payment = $5,000. You have just made a payment and decided to pay the loan off by repaying the outstanding balance. a) what is payoff amount if you have owned the car for one year (so there are 4 ...
  81. Finance

    EMAR expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20-year cash flow? Use an 7% discount rate.
  82. Chemistry H

    60.0 grams of Th-210 with a half life of 50,000 years is allowed to decay for 250,000 years. How much of the original quantity remains? In addition, Th-210 decays via beta emission. Write the equation for its transmutation.
  83. Finance

    Ambrin Corp. expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20 year cash flow. Use a 11% discount rate.
  84. Finance

    ABC corp. expects to receive $2000 per year for years and $3500 per year for the next 10 years. what is the percentage value of this 20 years cash flow? use an 7% discount rate
  85. Maths

    ABC corp. expects to receive $2000 per year for years and $3500 per year for the next 10 years. what is the percentage value of this 20 years cash flow? use an 7% discount rate
  86. FINANCE

    8. Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: 1R1 = 5 percent, E(2r1) = 6 percent, E(3r1) = 7.5 percent E(4r1) = 6.85 percent Using the ...
  87. Math

    You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physic. You purify a sample of 2 grams.One of you colleges steals half of it, and 3 days later you find that 0.1 grams of the radioactive material is still ...
  88. finance

    The Blinkelman Corporation has just announced that it plans to introduce a new solar panel that will greatly reduce the cost of solar energy. As a result, analys now expect the company’s earnings, currently (year 0) $1 per share to grow by 50 percent per year for the next ...
  89. finance

    The Blinkelman Corporation has just announced that it plans to introduce a new solar panel that will greatly reduce the cost of solar energy. As a result, analys now expect the company’s earnings, currently (year 0) $1 per share to grow by 50 percent per year for the ...
  90. Java Computer Science

    So in math, a restriction can be set. For example 30<x<60. So I'm trying to do this in a Java else if statement. else if (x>30 && x<60) {, will that do the same thing. Because I did that in my program but I'm getting my desired output twice. I'm suspecting this is ...
  91. Chemistry

    In 6.20 h a 100 g sample of ag 112 decays to 25 grams. what is the half life of ag 112. I think the answer is 3.10 but I'm not sure. Thanks in advance =)
  92. college algebra

    Suppose that the Russian population is declining by 0.48% each year, and continues to decline at this rate every year. a.) what is the overall 'growth' factor (really a decline factor) for 40 years of population decline? As a percentage of the current population, what will the...
  93. Finance

    Consider the following scenario: John buys a house for $150,000 and takes out a five year adjustable rate mortgage with a beginning rate of 6%. He makes annual payments rather than monthly payments. Unfortunately for John, interest rates go up by 1% for each of the five years ...
  94. Finance

    Consider the following scenario: John buys a house for $150,000 and takes out a five year adjustable rate mortgage with a beginning rate of 6%. He makes annual payments rather than monthly payments. Unfortunately for John, interest rates go up by 1% for each of the five years ...
  95. Pre-Cal

    The population of Las Vegas, Nevada in 2000 was 478,000 and is increasing at the rate of 6.28% per year. At this rate, when will the population reach 1 million people? a)1.51 years b)2.32 years c)12.12 years d)10.84 years
  96. Math

    Suppose that a certain material has a half life of 25 years, and there are A(t)=10(1/2)^t/25 grams remaining after t years. find: i) initial amount i) Amount after 80 years Solutions i) A(0)=10(1/2)^(0/25) =10(1/2)^0 =10(1) =10 ii)A(80)=10(1/2)^(80/25) =10(1/2)^(16/5) =10(0....
  97. Maths

    Can you help me with this? I don't know how to figure it out. the population growing at an annual rate r will triple in a time t given by the formula t = ln 3/r If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to ...
  98. chemistry

    an original sample of K-40 has a mass of 25.00 grams. After 3.9x 10 to the ninth years, 3.125 grams of the original sample remains unchanged. What is the half-life ok K-40 in minutes? Is it 6.8328 x 10 to the 14th
  99. Pre Calculus

    17. population growing at an annual rate r will triple in a time t given by the formula t = ln 3/r If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple? a. 6 . 6 years b. 1 years c. 5 . 3 years d. 2 . 2 years e...
  100. chemistry

    a 15g sample of gold-198 decays in 3g in 6 days. how much will be left after 8 days?
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