An element with mass 490 grams decays by 28.6% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?

This problem describes an exponential decay process, where the mass of the element decreases by a fixed percentage per minute. The general formula for exponential decay is:

\[
M(t) = M_0 \times (1 - r)^t
\]

Where:
- \( M(t) \) is the mass remaining after \( t \) minutes.
- \( M_0 \) is the initial mass of the element (490 grams).
- \( r \) is the decay rate per minute (28.6% or 0.286).
- \( t \) is the time in minutes (16 minutes in this case).

Now, let's calculate the mass remaining after 16 minutes:

\[
M(16) = 490 \times (1 - 0.286)^{16}
\]

First, simplify the decay factor:

\[
1 - 0.286 = 0.714
\]

Thus, the formula becomes:

\[
M(16) = 490 \times 0.714^{16}
\]

Now let's compute the remaining mass.

The remaining mass of the element after 16 minutes is approximately 2.2 grams, to the nearest tenth.

Would you like any further details or have any questions about the solution?

Here are 5 related questions to expand on this concept:
1. What would the remaining mass be after 10 minutes?
2. How would the formula change if the decay rate was compounded every second instead of every minute?
3. How long would it take for the mass to decay to less than 1 gram?
4. What is the half-life of the element, given this decay rate?
5. How much of the element remains after 5 minutes?

**Tip:** Exponential decay problems often use the same structure as compound interest problems but with decay rather than growth.

Solve an exponential decay problem where an element with an initial mass of 490 grams decays by 28.6% per minute. Learn how to calculate the remaining mass after 16 minutes using the exponential decay formula. Suitable for students in Grades 10-12.

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