Example 3 from Algebra and Trigonometry, 6.7 Exponential and Logarithmic Models

Finding the Age of a Bone

A bone fragment is found that contains 20% of its original carbon-14. To the nearest year, how old is the bone?

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
We substitute $20 % = 0.20$ for $r$ in the equation and solve for $t :$
$\begin{array}{l} t = \frac{\ln (r)}{- 0.000121} & Use the general form of the equation . \\ = \frac{\ln (0.20)}{- 0.000121} \begin{matrix} \end{matrix} & Substitute for r . \\ \approx 13301 & Round to the nearest year . \end{array}$
The bone fragment is about 13,301 years old.

Your turn

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

Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?

How did it go?

Solution

Your turn

Solution

Your turn