Q10, exponential decay equation (with decay rate)

TL;DR

Plutonium-238 decays at a rate of 3.8% per year. After 25 years, approximately 40.90 grams will be left from a 50 gram sample.

Transcript

here we have plutonium-238 dkz at a rate of three point eight percent per year how much of a 50 gram sample will be left after 25 yrs first of all this right here is just the name of a chemical so the 238 it's not going to be folding our calculation so you can just read a question as a chemical decayed at this rate and how much do we have left afte... Read More

Key Insights

• ☠️ Plutonium-238 undergoes decay at a rate of 3.8% per year.
• ⌛ The formula for calculating the remaining amount after a certain time is A = A₀(1 + R)^T.
• ☠️ In this case, the decay rate is negative since the quantity of plutonium-238 decreases over time.
• ☠️ Converting a percentage rate to a decimal rate involves moving the decimal point two places to the left.
• 🍃 Using the given formula and values, approximately 40.90 grams will be left after 25 years from a 50 gram sample.
• ☠️ It is important to pay attention to the wording of the question to determine if the rate is positive or negative.
• 🎭 Calculations can be done using a calculator by inputting the given values and performing the necessary computations.

Questions & Answers

Q: What is the formula for calculating the amount of plutonium-238 remaining after a certain time?

The formula is A = A₀(1 + R)^T, where A is the final amount, A₀ is the initial amount, R is the rate of decay, and T is the time in years.

Q: Why is the rate of decay, R, negative in this case?

The rate of decay, R, is negative because the amount of plutonium-238 decreases over time. Negative rate values indicate decreasing quantities.

Q: How do you convert a percentage rate to a decimal rate?

To convert a percentage rate to a decimal rate, you move the decimal point two places to the left. For example, 0.8% becomes 0.008 as a decimal rate.

Q: What is the amount of plutonium-238 remaining after 25 years from a 50 gram sample?

After 25 years, approximately 40.90 grams of plutonium-238 will be left from a 50 gram sample, given a decay rate of 3.8% per year.

Summary & Key Takeaways

• Plutonium-238 decays at a rate of 3.8% per year.

• The formula for calculating the remaining amount after a certain time is A = A₀(1 + R)^T.

• Using the formula, the amount of plutonium-238 left after 25 years from a 50 gram sample is approximately 40.90 grams.