Half Life: The level of radioactivity on the site of a nuclear explosion is decaying exponentially.?

Question

The level of radioactivity on the site of a nuclear explosion is decaying exponentially. The level measured in 1930 was found to be 0.8 times the level measured in 1920. What is the half-life.

Answer 1

1920 and 1930 ???  Whoever wrote that test may be a good physicist but (s)he is no historian.

In 10 years the value droped to .8. in 20 years it will drop to .64  In 30 years it will go to .512 Half liife is about 32 years.

Answer 2

I think you want the exact formula for half-life.

T(half) = (t-t0)*ln(2) / ln(x0/x(t)) = 10*ln(2)/ln(1/0.8) = 31.02684 yr.