A quantity starts at 29,000 and is exponentially decaying at the rate of 3% per week.  What is left of that quantity after the 6th week has passed?

To calculate the remaining quantity after 6 weeks of exponential decay, we can use the formula for exponential decay:

\[
Q(t) = Q_0 \cdot (1 - r)^t
\]

Where:
- \( Q(t) \) is the remaining quantity after time \( t \),
- \( Q_0 \) is the initial quantity,
- \( r \) is the decay rate (in decimal form),
- \( t \) is the time in weeks.

Given:
- Initial quantity \( Q_0 = 29,000 \),
- Decay rate \( r = 3\% = 0.03 \),
- Time \( t = 6 \) weeks.

Substituting the values into the formula:

\[
Q(6) = 29,000 \cdot (1 - 0.03)^6
\]

Let's calculate the result.After 6 weeks of exponential decay at a rate of 3% per week, approximately 24,156.19 units of the original quantity remain.

Would you like further details or clarifications on this? 

Here are 5 related questions to expand on this topic:
1. How would the remaining quantity change if the decay rate were 5% instead of 3%?
2. What would be the quantity after 10 weeks with the same 3% decay rate?
3. How do you calculate the decay constant for exponential decay?
4. Can the exponential decay model be applied to population growth? If so, how?
5. How does exponential decay compare to linear decay in terms of speed?

**Tip**: Exponential decay decreases faster in the early periods compared to later ones due to its nature of shrinking by a fixed percentage of the remaining amount.

A quantity starts at 29,000 and is exponentially decaying at the rate of 3% per week. What is left of that quantity after the 6th week has passed?

Learn how to calculate the remaining quantity after 6 weeks of exponential decay at a rate of 3% per week, starting with 29,000 units. This solution covers key exponential decay formulas and concepts, suitable for students in Grades 9-12.

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