Help on exponential Decay

[borinbuscadecuartos]

Hey everyone i am having a little trouble with this problem. The question is the half life of cesium-137 is 30.2 years. If today we have 750 pounds of radioactive cesium. How much will be lost over the next 500 years.

ok this is what i have so far.


I put 1/2A=AB raised by 30.2
then i got 1/2 = B raised by 30.2 because the a's cancel eachother out.
so i solve for B, however after this i am lost
i know i must put this in a logarithm to find how much will be lost in 500 years but can someone please help me

 

[wjm11]

the half life of cesium-137 is 30.2 years. If today we have 750 pounds of radioactive cesium. How much will be lost over the next 500 years.

ok this is what i have so far.


I put 1/2A=AB raised by 30.2
then i got 1/2 = B raised by 30.2 because the a's cancel each other out.

1/2A=AB raised by 30.2 Why!?!

It looks as though you’re trying to follow some “steps” to arrive at an answer, without having an understanding of the underlying equation. Let’s start by looking at a general form of an exponential function and figuring out what the various parts mean:

y = a(b)^x

The a and b are constants that depend on the particular problem. The x and y are the variables, and x is the exponent of b; if we put in a value for x, we can calculate a value for y (assuming we already know what the constants, a and b, are).

In “half-life” problems, we’re using the above equation. The “a” constant is our starting amount. “b” is set to ½.

The “x” is the “amount of time we’re interested in” divided by the half-life period. Dividing the elapsed time by the half-life tells us the number of half-lives that have gone by.

The “y” is the final amount after a given time period has elapsed:

Final amount = (initial amount)(1/2)^[(elapsed time)/(half-life)]

In your specific problem, we’re given the all the information on the initial amount, half-life, and elapsed time:

Final amount = (750)(1/2)^[500/30.2]