Question

Arianna finds some fossil bones while digging in her backyard. Could they be dinosaur bones? Using carbon dating, she determines that 3% of the original radioactive carbon-14 is still radioactive. (The rest has decayed to
nitrogen-14.)

Approximately how many half-lives have occurred?

The half-life of carbon-14 is 5,730 years. This means that the animal died approximately
years ago.

Answer 1

Let f = 0.03 = (1/2)^n. Then
n = ln(0.03)/ln(1/2) ≈ 5.06 half-lives.

Time = n × 5730 ≈ 5.06 × 5730 ≈ 28,990 ≈ 29,000 years ago.

So no — this is far too recent to be a dinosaur (dinosaurs died out ~66 million years ago).