# Find the half-life (in hours) of a radioactive substance that is reduced by 30 percent in 40 hours.

128,424 results
1. ## calculus

A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? (b) How long would it take the sample to decay to 65% of its original amount?

2. ## math calculus

Find the half-life (in hours) of a radioactive substance that is reduced by 30 percent in 40 hours.

3. ## precalculus

Twenty percent of a radioactive substance decays in ten years. By what percent does the substance decay each year?

4. ## Calculus-Modeling Equations

An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 39 percent. 1.What is the half-life of the element? 2.How long will it take for a sample of 100 mg to decay to 46 mg?

5. ## Exponential Modeling

The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 100 grams of this substance. How many grams of the substance would be left after a week?

6. ## Math

A radioactive substance decays exponentially. A scientist begins with 130 milligrams of a radioactive substance. After 20 hours, 65 mg of the substance remains. How many milligrams will remain after 24 hours?

7. ## precal

If the half-life of a certain radioactive substance is 2000 years, estimate how many years must elapse before only 35% of the radioactive substance remains?

8. ## pre calculus

if 17 percent of a radioactive substance decays in 12 hours, what is the half-life of the substance? Round your answer to one decimal place.

9. ## math

An unknown radioactive element decays into non-radioactive substances. In 100 days the radioactivity of a sample decreases by 64 percent. a)(a) What is the half-life of the element? half-life: b)How long will it take for a sample of 100 mg to decay to 51

10. ## Math

The half-life of radioactive strontium-90 is approximately 32 years. In 1961, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 8

11. ## Math, Calculus

Assume a quantity decreases by 6.7% in 8.6 hours. What is the half-life of the substance? (in hours) (Your answer should be accurate to two decimal places.)

12. ## Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay

13. ## mathematics

Find the half-life (in hours) of a radioactive substance that is reduced by 30 percent in 80 hours

14. ## 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

15. ## 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

16. ## Physical Science- Help Please!

Suppose that you are given a 100 gram sample of a radioactive substance with a half-life of 32 days. How many grams will be left after 192 days?

17. ## 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

18. ## Calculus

a certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, is given by the function f(t)=3e^-3t. What is the rate of decay of the substance after half a year: I first found the derivative of

19. ## Calculus

A certain radioactive material is known to decay at a rate proportional to the amount present. A block of this material originally having a mass of 100 grams is observed after 20 years to have a mass of only 80 grams. Find the half-life of this radioactive

20. ## 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

21. ## math with application

If 12 % of a radioactive substance decays in 7 hours, what is the half-life of the substance? Carry out all calculations exactly, then round the final answer to three decimal places. The half life is what hours?

22. ## half-life

If 250mg of a radioactive element decays to 200mg in 48 hours, find the half-life of the element. ln(No/N) = kt No=250 mg N = 200 mg t = 48 hours. Solve for k, then put k into the following equation and solve for t1/2. k = 0.693/t1/2

23. ## AP science

You have 180 g of a radioactive substance. It has a half-life of 265 years. After 1,325 years, what mass remains?

24. ## Science

Radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.6)^(-t). a) Determine the function A’, which represent the rate of decay of the substance. b) what is the half-life for

25. ## Stats

A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. If the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 and 900

26. ## college algebra

if 60% of a radioactive element remains radioactive after 300 million years, then what percent remains radioactive after 500 million years? what is the half-life of this element?

27. ## college algebra

An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 40% more of the substance? (Round your answer to one decimal place.) ____hr

28. ## Chemistry

Which radioactive sample would contain the greatest remaining mass of the radioactive isotope after 10 years? A. 2.0 grams of 198 Au B. 2.0 grams of 42 K C. 4.0 grams of 32 P D. 4.0 grams of 60 Co By the way the numbers next to the elements are their

29. ## math

8. The half-life of a certain radioactive material is 71 hours. An initial amount of the material has a mass of 722 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 17 hours. Round

30. ## Math

Find the half-life (in hours) of a radioactive substance that is reduced by 10 percent in 5 hours.

31. ## Pre-calculus

Initially 600 milligrams of a radioactive substance was present. After 7 hours the mass had decreased by 3%. Construct an exponential model A(t) = A0ekt for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24

32. ## Chem

Radioactive 24Na with a half-life of 14.8 hours is injected into an animal in a tracer experiment. How many hours will it take for the radioactivity to fall to 12.5% of its original intensity? I am confused on what number to start with

33. ## math

Show that if a radioactive substance has a half life of T, then the corresponding constant k in the exponential decay function is given by k=-ln(2)/T I'm confused about how to show that that is true.

34. ## Calculus

The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is the time in years. A. If

35. ## 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?

36. ## Algebra

A radioactive substance decays exponentially. A scientist begins with 140 milligrams of a radioactive substance. After 21 hours, 70 mg of the substance remains. How many milligrams will remain after 35 hours?

37. ## calculus

assume the half-life of the substance is 31 days and the initial amount is 183.9 grams. (a) Fill in the right hand side of the following equation which expresses the amount A of the substance as a function of time t (the coefficient of t in the exponent

38. ## Pre calc

If 250 mg of a radioactive element decays to 200 mg in 48 hours, find the half-life of the element

39. ## Algebra 2

A radioactive substance decays at a rate of y = ae^-0.1483t, where t in in hours. Find the half-life of the substance. How do I solve this problem if I am only given the constant.

40. ## calculus

Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of approximately 5730 years. Using

41. ## Alg2

Radioactive iodine is used to determine the health of the thyroid gland. It decays according to the equation y=ae -0.0856t where t is in days. Find the half-life of this substance. Round to the tenths place.

42. ## chemistry

if you start with 100mg of radioactive material that has a half life of one hour, how many mg's of radioactive material would you have in 10.2284952 hours?

43. ## Math - D.E.Q.

The half-life of a radioactive isotope is the amount of time it takes for a quantity of radioactive material to decay to one-half of its original amount. i) The half-life of Carbon 14 (C-14) is 5230 years. Determine the decay-rate parameter  for C − 14.

44. ## physical science

A certain radioactive substance has a half-life of 1 hour. If you start with 1 gram of the material at noon, how much will be left at 3:00 P.M.? At 6:00 P.M.? At 10:00 P.M.?

45. ## Math-Exponential Decay

A lab technician had 58 grams of a radioactive substance. Ten days later, only 52 grams remained. Find the half-life of the radioactive substance.

46. ## Science

What fraction of the original activity of a radioactive substance will remain at the end of half-life?

47. ## physics

Radioactive nuclei are produced in an irradiated sample at the rate of 10 s-1. If the number in the sample builds up to a maximum of 1000, calculate the mean life and the half-life of the radioactive nuclei Using dN / dt = P - λ N dN / dt = 1000n /10/ 1 =

48. ## Calculus

The amount remaining of a radioactive substance after t hours is given by A(t) = 100ekt. After 12 hours, the initial amount has decreased by 4%. How much remains after 48 hours? What is the half-life of the substance?

49. ## Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay

50. ## math

Iodine-131 is a radioactive isotope used in the treatment of thyroid conditions. It has a half-life of 8 days. Half-life is the amount of time it takes for half of the substance to decay (or disappear). If a patient is given 20 mg of iodine-131, how much

51. ## College Calculus

A radioactive substance has a half-life of 27 years. Find an expression for the amount of the substance at time t if 20 grams were present initially.

52. ## chemistry

Some radioactive nuclides have very short half-lives, for example, I-31 has a half-life of approximately 8 days. Pu-234, by comparison has a half-life of 24,000 years. Explain why both of these examples are dangerous, even though their half-lives are very

53. ## math

You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physics. You purify a sample of 2 grams. One of your colleagues steals half of it, and eight days later you find that 0.1 gram of the

54. ## Science

A radioactive substance is found to register 1000 counts per second on a Geiger counter. Twenty-four hours later it registers 125 counts per second. What is its half-life?

Radioactive decay is the process by which an unstable element transforms into different element, typically releasing energy as it does so. For 500g of a radioactive substance with a half-life of 5.2 hours, the amount remaining is given by the formula

56. ## Exponential decay

Show that if a radioactive substance has a half life of T, then the corresponding exponential decay function can be written as y=y0e^kt

57. ## math30

The mass of a radioactive sample is represented in the graph below. The initial mass of 32 mg decays to 8 mg after 21 hours. 1)What is the half-life of the radioactive sample, in minutes? 2)Solve each equation. a. 4 8x-1 = 8 b. 3^(2x-5) = 1/27x

58. ## Chemistry

Mefenamic acid (Ponstan Forte) has a half life of 2 hours. Naproxen has a half life of 12 to 17 hours. Both are anti inflammatory drugs of apparently similar nature but could someone please explain the difference in half life? Thank you Mike

59. ## chemistry

The half-life of C14 radioactive is 5760 yr. After how much time will 200 mg C14 sample be reduced to 25 mg?

60. ## Math

An unknown radioactive substance has a half-life of 124 years. How long will it take a 67 grams sample to degrade to 18 grams?

61. ## College algebra

If 70% of a radioactive element remains radioactive after 400 million years , then what percent remains radioactive after 600 million years? What is the half-life of this element

62. ## Calculus

The half-life of radioactive strontium-90 is approximately 31 years. In 1960, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 11

63. ## Science

A human body required 0.01 m activity of radioactive substance after 24 hours .Half li of radioactive substance is 6 hours .Then injection of maximum activity of radioactive substance that can be injected is : a). 0.08 b). 0.04 c). 0.16 d). 0.32

64. ## Math

A radioactive substance decays to the formula N=8e^-0.6t , where N is the number of milligrams present after t hours. Determine the initial amount of the substance to the nearest 10th of an hour, determine the half life of the substance, and determine the

65. ## chm

An unknown radioactive substance has a half-life of 3.20 . If 34.8 of the substance is currently present, what mass was present 8.00 hours ago?

66. ## math

A researchr assistant made 160mg of a radioactive, and found that there was only 20mg left after 45hours. a) What is the half-life of this substance? b) Write a function to represent the amount of substance left after x hours c) If the researcher kew he

67. ## math

if the rate for radioactive decay for a substance is r=-.0063 and time is being measured in days how do you find the half-life of the substance to the nearest hour?

68. ## Math/Calculus

After 5 days, a particular radioactive substance decays to 37% of its original amount. Find the half life of this substance. Is this right? Th= ln 2/ln(1/.37) x 5 days

69. ## Math

the half life of a radioactive substance is one day. You have 100 grams. how much of the substance would be left after a week?

A radioactive substance has a half-life of 4 days. Suppose we have 800 mg of this substance. a) Find the equation of the mass remaining after t days. Use the exact value for k not a decimal approximation. b) Rounding your answer to the nearest tenth of a

A radioactive substance has a half-life of 4 days. Suppose we have 800 mg of this substance. a) Find the equation of the mass remaining after t days. Use the exact value for k not a decimal approximation. b) Rounding your answer to the nearest tenth of a

72. ## Physics

A radioactive substance has a half life of 60s.what fraction of the original substance would you expect to exist after 180s.

73. ## Physics

A radioactive substance decays from 2.0kg to 1.6kg in 156 days. What is the decay constant and the half life of the substance?

74. ## Pre Calculus

Exponential Growth and Decay Find the half-life of a radioactive substance that decays by 5% in 9 years.

75. ## math

The half life of the radio active substance is the time require the half the substance to decay. the mount A ( in grams) of 100 gram sample of a radio active substance remaining after t half lives by A equals to 100 (0.5) t. suppose the substance has a

76. ## math

an extremely volatile substance, Ofnetite, has a half-life of 25 minutes. Find the percentage decrease of this substance in the first two hours.

77. ## pre calc

You have a sample of a certain radioactive substance. After two days, thirty percent of the sample has decayed. What is the half-life of the material and how much will have decayed after a week?

78. ## pre calc

You have a sample of a certain radioactive substance. After two days, thirty percent of the sample has decayed. What is the half-life of the material and how much will have decayed after a week?

79. ## Engineering Math

An unknown radioactive element decays into non-radioactive substances. In 120 days the radioactivity of a sample decreases by 59 percent. What is the half life of the element? How long will it take for a sample of 100 mg to decay to 77 mg? The answer is

80. ## 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

81. ## Alg2

Radioactive iodine is used to determine the health of the thyroid gland. It decays according to the equation y=ae -0.0856t where t is in days. Find the half-life of this substance. Round to the tenths place.

82. ## pre-calculus

Initially 700 milligrams of a radioactive substance was present. After 2 hours the mass had decreased by 5%. Construct an exponential model A(t) = A0ekt for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24

83. ## physics

The half-life of a certain radioactive isotope is 32 hours.What fraction of the sample would remain after 16 hours?(a)0.50(b)0.25(c)0.62(d)0.71

84. ## Calculus

Write a differential equation to model the situation given. Do not solve. The radioactive substance neptunium-139 decays to 73.36% of its orginal amount after 24 hours. How long would it take for 43% of the original neptunium to be present? What is the

85. ## Math

The percent P of a radioactive substance remaining after time t weeks is given by the formula p = 100.(0.5)^1/20 the percent to the nearest whole number of radioactive substance remaining after 30 weeks is?

86. ## physics

Calculate the half-life of a radioactive substance that decays by a factor of 3 in concentration every 1 million years

87. ## Physics

Suppose a hypothetical radioactive nucleus (Hy) has a half-life of 10 days. If we have 80 gms of the substance at the start of an experiment, how many gms of the substance will remain undecayed after 30 days

88. ## chemistry

A particular radioactive substance has a half-life of 4 minutes. How long will it take for 250 g of this radioactive material to decay to less than 0.1g? 24 min 36 min 40 min 48 min 72 min I got 32 min but that not one of the choices. Please help

89. ## Math, Calculus

Assume the half-life of a substance is 34 days and the initial amount is 116.399999999999 grams. (a) Fill in the right hand side of the following equation which expresses the amount A of the substance as a function of time t (the coefficient of t in the

90. ## Math

Suppose f(t) = P0e^-0.3t grams of radioactive substance are present after t seconds. If 200 grams of substance are present initially, how much is present after 4 seconds? What is the half-life of the substance?

91. ## linear/exponential

This question involves the half-life formula. In this exercise, we are to give a half-life for an exponentially decaying quantity. Need answer to the following: The half-life of a drug in the bloodstream is 4 hours. By what factor does the concentration of

92. ## Physics HELP HELP

(for some reason I keep getting this wrong. I put 90 for c, 5.6 for h and 22 for M(x), Then I took the natural log of both sides, but I keep getting it wrong) The mass of a radioactive element at time x is given by the equation below, where c is the

93. ## science

A 10g sample of radioactive substances is lift to decay for five half-lives. How much of the radioactive substance remains?

94. ## Calculus

The half-life of radioactive strontium-90 is approximately 31 years. In 1960, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 11

95. ## Algebra

A radioactive kind of nitrogen has a half life of 10 minutes. If you start with 64 grams of the substance, how much will be left after 20 minutes?

96. ## Science

If a 20 gram sample of a radioactive substance has a half-life of 6000 years, how many grams would be present after 18000 years?

97. ## Physics (Inside the atom)

A sample of radioactive isotope I is to be used for medical diagnosis of the kidneys. The isotope has a half-life of 8.0 days, and the sample is required to have an activity of 8 x 10^5 per second at the time it is given to the patient. Calculate the mass

98. ## Physcis 30

Q1) If there are 100 radioactive atoms with a half-life of 30 seconds, how many radioactive atoms will remain after one half-life (30 seconds)? How many will remain after two half-lives (60 seconds)? Three half-lives? So basically, after 30 seconds it will

99. ## Math

The half-life of radioactive strontium-90 is approximately 28 years. In 1962, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 6

100. ## college algebra

Use a calculator to help solve the problem. An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 40% more of the substance? (Round your answer to one decimal place.) ____hr