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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.
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Opts 2om OMedle 31 80 The radoactive isotope of lead, Pb-209, decays at a rate propotion answer to tee decmal alaces.) to the amount present at time tand has a haf-afe of 3.3 hours. If 1 gram of ths sotope is present intialy, how long wEt take for 70% of the lent to decay? (Raund your
Opts 2om OMedle 31 80 The radoactive isotope of lead, Pb-209, decays at a rate propotion answer to tee decmal alaces.) to the amount...
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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...
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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)
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Part III continued 6. The rate of decay of a radioactive substance is proportional to the amount present. Today we have 10 grams of a radioactive substance. Given that 1/3 of the substance decays every 5 years, how much will be left 17 years from today? 7. Evaluate the following integrals: a) 5-4x-x2 dx, x2-x3
Part III continued 6. The rate of decay of a radioactive substance is proportional to the amount present. Today we have 10 grams of a...
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(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
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(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...
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(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...
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In this question, we ask you to solve the differential equation dy (3x-6)2-(2y-s) dx satisfying the initial condition 4.1 (1 mark) Hopefully, you have observed that the d.e. is separable. Thus, as a first step you need to rearrange the d.c. in the form for appropriate functions fy) and g(x) Enter such an equation, below y) dy-g(x) dx Note. The differentials dx and dy are simply entered as dx and dy, respectively separated d.e You have not attempted this yet...
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Solve the equation (3x?y - 1)dx + (y - 4x?y-2)dy = 0 is an arbitrary constant, and V by multiplying by the integrating factor. An implicit solution in the form F(x,y) = C is = C, where (Type an expression using x and y as the variables.)
Opts 2om OMedle 31 80 The radoactive isotope of lead, Pb-209, decays at a rate propotion answer to tee decmal alaces.) to the amount present at time tand has a haf-afe of 3.3 hours. If 1 gram of ths sotope is present intialy, how long wEt take for 70% of the lent to decay? (Raund your
Opts 2om OMedle 31 80 The radoactive isotope of lead, Pb-209, decays at a rate propotion answer to tee decmal alaces.) to the amount...
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...
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)
Part III continued 6. The rate of decay of a radioactive substance is proportional to the amount present. Today we have 10 grams of a radioactive substance. Given that 1/3 of the substance decays every 5 years, how much will be left 17 years from today? 7. Evaluate the following integrals: a) 5-4x-x2 dx, x2-x3
Part III continued 6. The rate of decay of a radioactive substance is proportional to the amount present. Today we have 10 grams of a...
(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
(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...
In this question, we ask you to solve the differential equation dy (3x-6)2-(2y-s) dx satisfying the initial condition 4.1 (1 mark) Hopefully, you have observed that the d.e. is separable. Thus, as a first step you need to rearrange the d.c. in the form for appropriate functions fy) and g(x) Enter such an equation, below y) dy-g(x) dx Note. The differentials dx and dy are simply entered as dx and dy, respectively separated d.e You have not attempted this yet...
Solve the equation (3x?y - 1)dx + (y - 4x?y-2)dy = 0 is an arbitrary constant, and V by multiplying by the integrating factor. An implicit solution in the form F(x,y) = C is = C, where (Type an expression using x and y as the variables.)