An element with mass 590 grams decays by 19.5% per minute. How much of the element is remaining after 15 minutes, *to the nearest 10th of a gram*?

To find out how much of the element remains after 15 minutes, given that it decays by 19.5% per minute, we can use a similar exponential decay formula:

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

Where:
- \( M \) is the remaining mass after \( t \) minutes,
- \( M_0 \) is the initial mass,
- \( r \) is the decay rate per minute (expressed as a decimal),
- \( t \) is the number of minutes.

Given:
- \( M_0 = 590 \) grams,
- \( r = 19.5\% = 0.195 \),
- \( t = 15 \) minutes.

Substitute the values into the formula:

\[
M = 590 \times (1 - 0.195)^{15}
\]

Now let's calculate the remaining mass.The remaining mass of the element after 15 minutes will be approximately 22.8 grams.

Would you like more details or have any further questions?

Here are some related questions you might find interesting:
1. How long will it take for the mass of the element to decrease to 10 grams?
2. What is the half-life of the element based on the given decay rate?
3. How would the remaining mass change if the decay rate was 10% instead of 19.5%?
4. What is the formula for exponential growth, and how does it compare to exponential decay?
5. How can we determine the decay constant from the given percentage?
6. If the initial mass were doubled, how would the final remaining mass change?
7. How does the concept of half-life apply to radioactive decay?
8. What are some real-world applications of exponential decay in science?

**Tip:** In decay problems, be sure to use the correct time units and ensure the decay rate matches those units for accurate results.

Learn how to calculate the remaining mass of an element decaying at 19.5% per minute from an initial mass of 590 grams after 15 minutes. Get a detailed solution using the exponential decay formula. Suitable for high school students studying decay rates.

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