Question

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.

Answer 1

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)