anonymous
  • anonymous
Radium decreases at the rate of 0.0428 percent per year. a. What is its half-life? (A half-life of a radioactive substance is defined to be the time needed for half of the material to dissipate. b. Write a recurrence relation to describe the decay of radium, where rn is the amount of radium remaining after n years. c. Suppose that one started out with 2 grams of radium. Find a solution for the discrete dynamical system illustrating this process and give the value for r(100), the amount remaining after 100 years.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
set \[e^{-0.0428t}=\frac{1}{2}\] solve for t
anonymous
  • anonymous
how to solve? X2 +7x + 12 = 0
mathmagician
  • mathmagician
Suppose, that at the beginning there are 1000g of radium. After a year there will be 999.572 g. And you want to know, when there will be 500 g of radium. So, use formula\[N _{0}=Ne ^{kt}\]. So, you get \[1000=999.572e ^{k*1}\]. \[k=\ln 0.999572=-0.000428\]. Now, when you know k, you can calculate lifetime:\[0.5=e ^{-0.000428*t}\], \[\ln(0.5)=-0.000428t\] And lifetime is 1619.5 years.

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