The level of radioactivity on the site of a nuclear explosion is decaying exponentially. The level measured in 1980 was found to be 0.8 times the level measured in 1970. What is the half-life.

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- May 12th 2008, 09:30 PMlilikoipssnHalf-Life
The level of radioactivity on the site of a nuclear explosion is decaying exponentially. The level measured in 1980 was found to be 0.8 times the level measured in 1970. What is the half-life.

- May 12th 2008, 09:44 PMearboth
Let L(0) denote the initial level of radiation and t the passed time. Then the level after t years is calculated by:

with k a constant typical for the decaying process.

From L(0) = 1 and L(10) = 0.8 you can derive k:

Now calculate the time which is necessary to reach only the half of the radioactivity:

Btw: That is a very optimistical result - May 12th 2008, 09:48 PMTheEmptySet