Calculating Continuous Decay

Radon-222 decays at a continuous rate of 17.3% per day. How much will 100 mg of Radon-222 decay to in 3 days?

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
Since the substance is decaying, the rate, $17.3 %$ , is negative. So, $r =$ The initial amount of radon-222 was $100$ mg, so $a = 100.$ We use the continuous decay formula to find the value after $t = 3$ days:

$\begin{array}{l} A (t) & = a e^{r t} & Use the continuous growth formula . \\ = 100 e^{- 0.173 (3)} \begin{matrix} \end{matrix} & Substitute known values for a, r, and t . \\ \approx 59.5115 & Use a calculator to approximate . \end{array}$
So 59.5115 mg of radon-222 will remain.

Your turn

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

Using the data in Example 12, how much radon-222 will remain after one year?

How did it go?