Question

Scientists are studying an 500 g. sample of a radioactive element. which has an annual decay rate of 11%.  How many grams of the sample would be left after 10 years? Round the answer to two decimal places.

Answer 1

Using the exponential decay formula A = P(1 - r)^n with P = 500 g, r = 0.11, and n = 10, approximately 156.91 grams of the radioactive sample would remain after 10 years.

Step-by-step explanation:

To calculate the amount of a radioactive element remaining after a certain period of time, one can use the formula for exponential decay, which is based on the decay rate. Since the decay rate is given as 11% per year, we can use this rate to find out how much of the sample would be left after 10 years.

The formula for exponential decay is:

A = P(1 - r)n

Where:

• A is the amount remaining after time n
• P is the initial amount of the substance
• r is the annual decay rate
• n is the number of years

In this case, P = 500 g, r = 0.11 (11%), and n = 10 years. We can calculate it as follows:

A = 500(1 - 0.11)10

Using a calculator, the amount remaining after 10 years, A, can be calculated as:

A ≈ 500 × 0.8910 ≈ 500 × 0.31381059609 ≈ 156.91 g

So, after 10 years, approximately 156.91 grams of the sample would be left.