An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, *to the nearest 10th of a gram*?

This problem involves exponential decay, and we can model it using the exponential decay formula:

\[
A(t) = A_0 \times (1 - r)^t
\]

where:
- \(A(t)\) is the amount remaining after time \(t\),
- \(A_0\) is the initial amount (780 grams),
- \(r\) is the decay rate (16.3% or 0.163),
- \(t\) is the time in minutes (16 minutes).

Now, let's compute how much of the element remains after 16 minutes.

\[
A(16) = 780 \times (1 - 0.163)^{16}
\]

I'll calculate this value for you.The remaining amount of the element after 16 minutes is approximately **45.3 grams** to the nearest tenth of a gram.

Would you like any additional details or have further questions?

Here are 5 related questions to consider:
1. How would the result change if the decay rate was 20% instead of 16.3%?
2. How can you determine the half-life of this element based on its decay rate?
3. What if the initial mass was 1000 grams—how much would be left after the same time?
4. How long would it take for the element to decay to just 10 grams?
5. What is the general relationship between decay rate and remaining mass over time?

**Tip:** The rate of exponential decay means that after a certain period, the element reduces by a fixed percentage, not a fixed amount.

An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?

Learn how to calculate the remaining mass of an element (initially 780 grams) decaying by 16.3% per minute after 16 minutes. This problem uses exponential decay formulas and covers algebraic concepts. Find out how much mass remains, rounded to the nearest 10th of a gram. Suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation