A certain radioactive material is known to decay at a rate proportional to the amount
present. If the initially there is 50 milligrams of the material present and after two
hours it is observed that the material has lost 10% of its original mass. Find
a) An expression for the mass of the material remaining at any time t
b) The mass of the material after 4 hours
c) The time rate at which the material has decayed to one half of its initial mass
Let the amount of radioactive material.
Given where is the proportionality constant.
Integrate
Let the initialamount of radioactive material.
Given
Substitute
a)
b)
c)
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