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If the average half-life of materials in a nuclear waste dump is 10,000 years, how long will it take until the radiation level reaches $5 \%$ of the present level?

43,220 years

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

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Given a half life of 10,000 years, how long will it take for the radiation to reach 5% of its present level? So we're going to be using this elapsed time formula here. So we have a half life of 10,000 years as given to us, multiplying that by the log of our beginning amount divided by our ending amount. So what I'm doing here is saying that we currently have whatever current amount is. This present level Is 100% of the present level. Because then we want to know how long it will take to get to this ending amount, which is 5% of the present level. Nothing gets divided by the log of two. Go ahead and calculate that and we can see that the time that we'll have that will have to elapse in order for that radiation to reach 5% of its present level is 43,000 219 years.

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