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.
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