121k views
2 votes
A sample of radium has a weight of 100 mg and a half-life of

approximately 6 years.
1. How much of the sample will remain after 6 years?
3 years?
1 year?
* Round all answers to the nearest 10th place.
2. Find a function f which models the amount of radium f(t), in mg,
remaining after t years.

1 Answer

4 votes

Final answer:

The remaining amount of the radium sample can be calculated using the formula A = A0 * (0.5)^(t / h), where A is the remaining amount, A0 is the initial amount, t is the time period, and h is the half-life. After 6 years, 50 mg of the sample will remain. After 3 years, 75 mg will remain. After 1 year, approximately 94.3 mg will remain.

Step-by-step explanation:

To find the amount of the sample that will remain after a certain period of time, we can use the formula:

A = A0 * (0.5)(t / h)

Where A is the remaining amount of the sample, A0 is the initial amount of the sample, t is the time period, and h is the half-life.

Using this formula, we can calculate the following:

  1. After 6 years: A = 100 mg * (0.5)(6 / 6) = 50 mg
  2. After 3 years: A = 100 mg * (0.5)(3 / 6) = 75 mg
  3. After 1 year: A = 100 mg * (0.5)(1 / 6) ≈ 94.3 mg

To find the function f(t) that models the amount of radium remaining after t years, we can use the formula:

f(t) = 100 mg * (0.5)(t / 6)

User Adel Boutros
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories