Question

example half-life problems:
if you have 10. grams of c - 14 (half - life = 5700 years) how much will remain after 5700 years?
after 11,400 years?
after 17,100 years?

Explanation:

Step1: Understand half - life concept

Half - life is the time required for a quantity to reduce to half of its initial amount.

Step2: Calculate for 5700 years

Since the half - life of C - 14 is 5700 years, after 5700 years (1 half - life), the amount remaining is \(10\times\frac{1}{2}=5\) grams.

Step3: Calculate for 11400 years

11400 years is \(11400\div5700 = 2\) half - lives. The amount remaining is \(10\times(\frac{1}{2})^2=10\times\frac{1}{4} = 2.5\) grams.

Step4: Calculate for 17100 years

17100 years is \(17100\div5700=3\) half - lives. The amount remaining is \(10\times(\frac{1}{2})^3=10\times\frac{1}{8}=1.25\) grams.

Answer:

After 5700 years: 5 grams.
After 11400 years: 2.5 grams.
After 17100 years: 1.25 grams.