## anonymous 5 years ago 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.

1. anonymous

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

2. anonymous

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

3. 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.