A radioactive isotope is unstable and will decay by emitting a particle, transforming into another isotope. The assumption used to model such situations is that the amount of radioactive isotope decreases proportionally to the amount currently present. (a) Let N(t) designate the amount of the radioactive material present at time tt and let N0 = N(0). Write and solve the IVP for the radioactive decay of radioactive material. (b) The half-life of a radioactive material is the time required for it to reach one-half of the original amount. What is the half-life of a material that in one day decays from 12mg to 9mg?
A radioactive isotope is unstable and will decay by emitting a particle, transforming into another isotope. The assumption used to model such situations is that the amount of radioactive isotope decreases proportionally to the amount currently present.
(a) Let N(t) designate the amount of the radioactive material present at time tt and let N0 = N(0). Write and solve the IVP for the radioactive decay of radioactive material.
(b) The half-life of a radioactive material is the time required for it to reach one-half of the original amount. What is the half-life of a material that in one day decays from 12mg to 9mg?
We have to use relation between decay rate and amount present at that time
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