Expert: Sherman D. - 1/24/2006

Question
Sherman-  First of all thanks so much for answering my question- that was really fast!!!!  However now I am having a hard time with my last two problems.

1)  Strontium-90 is a waste product from nuclear fission reactors.  It's half-life is 28 years and its decay model is A=A0e-0.024755t.  Suppose a nuclear accident occurs and releases 50 grams of strontium-90 into the bioshphere.  How long will it take for strontium-90 to decay to a level of 20 grams?


2)  If there is no restriction on food and living space, the rate of growth of a population of living organisms is proportional to the size of the population.  Thus, the formula A=A0e to the power of kt is appropriate.  Assume that in the absence of hunters, the deer population in New York State triples every 11 years.  Find the size of the herd of 500 deer after 5 years.

Sherman- your help is very apprecaited!!!  Thanks so much.  

Answer
1.)
A = A0e^(-.24755t)
20 = 50e^(-.24755t)
(2/5) = e^(-.24755t)
inverse e both sides
ln(2/5) = -.24755
t = (ln(2/5))/(-.24755)
t = 3.7014 years

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2.) I'm not 100%, but here goes
A = A0e^(kt)
A = 500e^(3(5/11))
A = 500e^(15/11)
A = 1955 deer

I would go to www.drmath.com, but they don't seem to reply to my questions that i send to them that you send when i have trouble. Sorry i couldn't help you much better. I use to have some online info that could tell me how to find it better, but i lost the link.