SOLUTION: strontium-90 is a waste product from nuclear fission reactors. It's half-life is 28 years and its decay model as A=A(subscript 0)e^-0.024755t. Suppose a nuclear accident occurs and

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Question 201783: strontium-90 is a waste product from nuclear fission reactors. It's half-life is 28 years and its decay model as A=A(subscript 0)e^-0.024755t. Suppose a nuclear accident occurs and releases 50 grams of strontium-90 into the biosphere. How long will it take for strontium-90 to decay to a level of 20 grams? I don't have a clue how to work this problem, can someone help?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
In general, if you have values for all but one of the variables in an equation, you can use the equation to find the last variable. In your equation you have three variables: A, A%5B0%5D and t. And you only know what you want A to be: 20. We want to find the time (t) so we need to know A%5B0%5D first.

To find A%5B0%5D, think about what happens when t=0. If t=0 then the exponent becomes 0. And what is e%5E0? Any number (except 0) raised to the 0 power is 1! So when t=0 your equation becomes A+=+A%5B0%5D. This means that A%5B0%5D represents the starting (t=0) amount! (Tip: This is what subscripts of zero often represent: a starting value for the variable with the same name without the subscript.)

Since we now know that A%5B0%5D is the starting amount of strontium-90 and we want to solve a problem for a starting amount of 50, we now have an equation we can use to find the answer:
20+=+50e%5E%28-0.024755t%29
We will now solve this for t. Start by dividing both sides by 50:
0.4+=+e%5E%28-0.024755t%29
Now find the natural logarithm (ln) of both sides:
ln%280.4%29+=+ln%28e%5E%28-0.024755t%29%29
The left side we can get from our calculator. The right side, if you understand logarithms well, simplifies easily. This is why we used ln to begin with. It is an easy way to get a variable out of an exponent. And we can't solve for t until it is out of the exponent.
-0.9162907318741551+=+-0.024755t
Now we just divide both sides by -0.024755:
37.0143701019654642+=+t
This tells us that it will take a little more than 37 years for 50g of strontium-90 to decay to 20g.