If 0.0898 of a radioactive substance remains after 80 days, find the half life of the substance?

0.0898^(x/80) = 0.5

Since x is a real number, then x/80 is a real number, so we have:

x/80 = log[0.0898](0.5)

x = 80*log[0.0898](0.5)

x =~ 23.007409210986788514053726376968

The equation you first need to solve is:

0.0898 = (1/2)^n, and "n" will be the number of half-life periods that have elapsed.

Since (1/2)^3 = 0.125 and (1/2)^4 = 0.0625, you know the "n" should come out between 3 and 4. One way to get it is:

log(0.0898) = n*log(1/2) =>

n = log(0.0898)/log(1/2) = 3.477.

So the 80 days is 3.477 half-life periods, which means the length of 1 half-life period would be 23.0 days.