Question

Arianna finds some fossil bones whip 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 reef 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

After 1 half-life: 50% gone. Total gone = 50%.  Amount left = 50%

After 2 half-lifes: 25% more gone. Total gone = 75%. Amount left = 25%

After 3 half-lifes: 12.5% more gone. Total gone= 87.5%. Amount left= 12.5%.

After 4 half-lifes: 6.25% more gone. Total gone= 93.75%. Amount left= 6.25%

After 5 half-lifes: 3.125% more gone. Total gone= 96.875%. Amount left= 3.125%.   Here we are !

Looks like right around 5 half-lifes have passed.

(5 half-lifes) x (5,730 years/half-life) = around 28,650 years .

= = = = = = = = = =

After 1 half-life: 1/2 gone. Total gone = 1/2. Amount left = 1/2.

After 2 half-lifes: 1/4 more gone. Total gone = 3/4. Amount left = 1/4.

After 3 half-lifes: 1/8 more gone. Total gone= 7/8. Amount left= 1/8.

After 4 half-lifes: 1/16 more gone. Total gone= 15/16. Amount  left= 1/16.

After 5 half-lifes: 1/32 more gone. Total gone= 31/32. Amount left= 1/32 = 3.125%.   Here we are !

Looks like right around 5 half-lifes have passed.

(5 half-lifes) x (5,730 years/half-life) = around 28,650 years .