A radioactive material decays with a rate proportional to the amount present at any instant. a)...
A radioactive material decays with a rate proportional to the
amount present at any instant.
a) Write and solve the differential equation.
b) Use the solution of the differential equation to solve the
following application problem.
Carbon 14 (14C) is a radioactive isotope of the carbon element and
has an approximate half-life of 5600 years. The fossil bones of an
animal were analyzed and found to contain one-tenth of the
radioactive 14C. Determine the approximate age of the bones
found.
Homework Answers
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A radioactive material decays with a rate proportional to the
amount present at any instant.
a)...
QUESTION 2 (a) A radioactive isotope, Pb-209, decays at a rate proportional to amount present at...
QUESTION 2 (a) A radioactive isotope, Pb-209, decays at a rate proportional to amount present at time t and has a half-life of 3.3 hours. If 1 gram of the isotope is present initially, how long will it take for 95% of the lead to decay?| (8 marks) (b) Form the differential equation associated with the given primitive y = Ae*' -1, by eliminating the arbitrary constants A. (4 marks) (C) Write the differential equation (1+ y2)dy + x =...
A certain radioactive substance decays at a rate proportional to its remaining mass M. a. Express this rate of decay as a differential equation. b. When a living organism dies it ceases to replac...
A certain radioactive substance decays at a rate proportional to its remaining mass M. a. Express this rate of decay as a differential equation. b. When a living organism dies it ceases to replace the carbon isotope C-14, and 48. the C-14 that is present decays with a half-ife of about 5730 years. If archeologists discover a fossilized bone that has 30% of the C-14 of a live bone, approximately how old is it?
A certain radioactive substance decays at...
(X) A radioactive material decays at a rate proportional to the population present at time t....
(X) A radioactive material decays at a rate proportional to the population present at time t. After 6 hours, the material has decreased by 87.5% (remained 12.5%). What is the half-life of this material? 24 a) d) 2 c) b) 4
A radioactive substance decays at a rate proportional to the amount present at ime t (in...
A radioactive substance decays at a rate proportional to the amount present at ime t (in hours). Initially, Ao grams of the substance was present, and after 10 hours, the mount has decreased by 20% How long will it take the substance to decay to 40? hat is the half life of this substance? Hint: the half-life is the time required for half of the initial substance to decay)
(2 points) The radioactive isotope carbon-14 is present in small quantities in all life forms, and...
(2 points) The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5592 years. Suppose C(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C' =-kC. k= (b) In 1988 three teams of scientists...
(1 point) The radioactive isotope carbon-14 is present in small quantities in all life forms, and...
(1 point) The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-ife of 5543 years. Suppose C(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C"=-kC k= (b) In 1988 three teams of scientists found...
Please slove both, will give upvote. Find the natue of a radioactive element, which decays according...
Please slove both, will give upvote.
Find the natue of a radioactive element, which decays according to the function A) - Age where is the time in years The half life of the element is years (Round to the nearest tenth) The amount of carbon 14 present in a paint after years is given by y = y, e d . The paint contains 27% of its carbon-14. How old are the paintings? The age of the paintings is (Round...
23) In the formula A(O)- Agekt, A is the amount of radioactive material remaining from an...
23) In the formula A(O)- Agekt, A is the amount of radioactive material remaining from an initial am a given time t, and k is to e decays at a rate of 0.3% annually. Determine hehalf ife of this isotope, to the nearest year is a negative constant determined by the nature of the material. A certain radioactive A) 231 yr B) 100 yr C) 167 y D) 2yr 24) The half-life of an element is 5.0 x і012 yr....
Using Python 3... Question 4: Carbon dating (3 points) Archaeologists use the exponential, radioactive decay of...
Using Python 3...
Question 4: Carbon dating (3 points) Archaeologists use the exponential, radioactive decay of carbon-14 to estimate the death dates of organic material. The stable form of carbon is carbon-12, and the radioactive isotope carbon-14 decays over time into nitrogen-14 and other particles. Carbon is naturally in all living organisms, and the carbon-14 that forms in the upper atmosphere enters into living things as long as they are taking in material (food, air, etc.) that contains carbon. We...
Applications of Exponential Equations Many real-life situations can be modeled by an exponential ...
ANSWER ALL PLEASE!
Applications of Exponential Equations Many real-life situations can be modeled by an exponential growth function of the form A(t) Ao ett constant that affects the rate of growth or decay, and t represents time. Using your knowledge of writing exponential equations that you did in the beginning of this chapter, what would A or an exponential decay function of the form A(t)-A ett where k represents the represent? 1. The amount of carbon-14 present in animal bones...
QUESTION 2 (a) A radioactive isotope, Pb-209, decays at a rate proportional to amount present at time t and has a half-life of 3.3 hours. If 1 gram of the isotope is present initially, how long will it take for 95% of the lead to decay?| (8 marks) (b) Form the differential equation associated with the given primitive y = Ae*' -1, by eliminating the arbitrary constants A. (4 marks) (C) Write the differential equation (1+ y2)dy + x =...
A certain radioactive substance decays at a rate proportional to its remaining mass M. a. Express this rate of decay as a differential equation. b. When a living organism dies it ceases to replace the carbon isotope C-14, and 48. the C-14 that is present decays with a half-ife of about 5730 years. If archeologists discover a fossilized bone that has 30% of the C-14 of a live bone, approximately how old is it?
A certain radioactive substance decays at...
(X) A radioactive material decays at a rate proportional to the population present at time t. After 6 hours, the material has decreased by 87.5% (remained 12.5%). What is the half-life of this material? 24 a) d) 2 c) b) 4
A radioactive substance decays at a rate proportional to the amount present at ime t (in hours). Initially, Ao grams of the substance was present, and after 10 hours, the mount has decreased by 20% How long will it take the substance to decay to 40? hat is the half life of this substance? Hint: the half-life is the time required for half of the initial substance to decay)
(2 points) The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5592 years. Suppose C(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C' =-kC. k= (b) In 1988 three teams of scientists...
(1 point) The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-ife of 5543 years. Suppose C(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C"=-kC k= (b) In 1988 three teams of scientists found...
Please slove both, will give upvote.
Find the natue of a radioactive element, which decays according to the function A) - Age where is the time in years The half life of the element is years (Round to the nearest tenth) The amount of carbon 14 present in a paint after years is given by y = y, e d . The paint contains 27% of its carbon-14. How old are the paintings? The age of the paintings is (Round...
23) In the formula A(O)- Agekt, A is the amount of radioactive material remaining from an initial am a given time t, and k is to e decays at a rate of 0.3% annually. Determine hehalf ife of this isotope, to the nearest year is a negative constant determined by the nature of the material. A certain radioactive A) 231 yr B) 100 yr C) 167 y D) 2yr 24) The half-life of an element is 5.0 x і012 yr....
Using Python 3...
Question 4: Carbon dating (3 points) Archaeologists use the exponential, radioactive decay of carbon-14 to estimate the death dates of organic material. The stable form of carbon is carbon-12, and the radioactive isotope carbon-14 decays over time into nitrogen-14 and other particles. Carbon is naturally in all living organisms, and the carbon-14 that forms in the upper atmosphere enters into living things as long as they are taking in material (food, air, etc.) that contains carbon. We...
ANSWER ALL PLEASE!
Applications of Exponential Equations Many real-life situations can be modeled by an exponential growth function of the form A(t) Ao ett constant that affects the rate of growth or decay, and t represents time. Using your knowledge of writing exponential equations that you did in the beginning of this chapter, what would A or an exponential decay function of the form A(t)-A ett where k represents the represent? 1. The amount of carbon-14 present in animal bones...
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