• 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.
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • chestercat
I got my questions answered at in under 10 minutes. Go to now for free help!
  • anonymous
set \[e^{-0.0428t}=\frac{1}{2}\] solve for t
  • anonymous
how to solve? X2 +7x + 12 = 0
  • 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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.