Using the Formula for Radioactive Decay to Find the Quantity of a Substance

How long will it take for ten percent of a 1000-gram sample of uranium-235 to decay?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$\begin{array}{l} y = 1000 e \frac{\ln (0.5)}{703,800,000} t \\ 900 = 1000 e^{\frac{\ln (0.5)}{703,800,000} t} & After 10% decays, 900 grams are left . \\ 0.9 = e^{\frac{\ln (0.5)}{703,800,000} t} & Divide by 1000 . \\ \ln (0.9) = \ln (e^{\frac{\ln (0.5)}{703,800,000} t}) & Take ln of both sides . \\ \ln (0.9) = \frac{\ln (0.5)}{703,800,000} t & ln (e^{M}) = M \\ t = 703,800,000 \times \frac{\ln (0.9)}{\ln (0.5)} years \begin{matrix} \end{matrix} & Solve for t . \\ t \approx 106,979,777 years \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

How long will it take before twenty percent of our 1000-gram sample of uranium-235 has decayed?

How did it go?