Radioactive Decay of an IsotopeDate: 01/05/98 at 23:43:57 From: Alf Butler Subject: Radioactive decay of an isotope Hi! I was working on a question for Precalculus over the decay of an the 226Ra isotope. I know it involves the use of logarithms (actually it can be an exponential function ae^x), but I'm having a little trouble fitting my information to my equation. If I have the half-life in years (1620) and the initial quantity (10g) then how do I find the amount of the isotope after 1000 years? Shouldn't I use the exponential decay model (y=ae^(-bx); b is greater than 0)? Hope you can help! Thanks so much. Date: 01/06/98 at 16:26:18 From: Doctor Jennifer Subject: Re: Radioactive decay of an isotope Hi Alf! First what you should do is make a chart with all the variables and what they stand for. That way it isn't so confusing. y - amount of 226 Ra a - initial amount of 226 Ra b - constant specific to 226 Ra x - time elapsed Now you need to figure out what you know and what you don't. y - ?? (that's your question) a - 10 g b - ?? x - 1000 years You now have 2 unknowns. You need to look at what other information was given. You have a half-life of 1620 years. How is that helpful? If you fill out the chart again you only have one unknown. y - 1/2 (see reason under a) a - 1 (Assume one. Then half of one is 1/2) b - ?? x - 1620 years Now if you plug all these values in the equation y = ae^(-bx), you can find your constant for b. Then go back to the original equation and your values should plug in perfectly. If you have any more problems don't hesitate to ask. We're here to help. -Doctor Jennifer, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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