Finding half life given decay rate

Hey guys, I'm working on a problem right now and I'm having some trouble.

The decay of a certain chemical is 9.3% per year. Using the exponential decay model P(t) = P_{0}^{-kt d} where k is the decay rate, and P_{0 }is the original amount of chemical find the half-life.

Thanks!

Re: Finding half life given decay rate

Just out of interest did you get the answer 7.1 years?

Re: Finding half life given decay rate

Yes that is the correct answer.

Re: Finding half life given decay rate

I'm a bit surprized- that formula doesn't make sense. If , then the "initial value" is , not . Did you mean ? And if is the initial value, t is the time, and k is the decay rate, what is "d"?

More common is the formula for decay. In one year, we will have . If the chemical decays 9.3% per year, P(1) should equal so . That is, k must satisfy so k= ln(.907)= -.0976.

Once you know that, the "half life" is the time until becomes . Solve which is the same as . Solve that for t.