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.

Question

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.

anonymous · Answer

set $$e^{-0.0428t}=\frac{1}{2}$$ solve for t

anonymous · Answer

how to solve? 
X2 +7x + 12 = 0

mathmagician · Answer

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.