The given function \( 3000(0.95)^t \) represents an exponential decay model where:

- The initial quantity is 3000.
- The decay factor is 0.95.
- \( t \) represents time.

To find the rate of decay as a percentage, we analyze the decay factor:

1. The decay factor is 0.95, which means that each period \( t \), the quantity decreases to 95% of its value from the previous period.
2. The decay rate is the percentage by which the quantity decreases each period.

The decay rate \( r \) is given by:

\[
r = 1 - \text{decay factor} = 1 - 0.95 = 0.05
\]

To express this as a percentage, multiply by 100:

\[
r = 0.05 \times 100 = 5\%
\]

**Therefore, the rate of decay is 5% per time period.**

Would you like more details on how exponential decay functions work, or do you have any specific questions?

Here are some related questions you might find interesting:
1. How would the function change if the decay rate was 10%?
2. What happens to the function as \( t \) approaches infinity?
3. How do you determine the half-life from an exponential decay function?
4. How would you model a situation with a decay rate that increases over time?
5. How does an exponential growth function compare to this decay function?

**Tip:** Exponential decay functions are often used to model processes like radioactive decay, depreciation of assets, and cooling of objects.

Explore the exponential decay model 3000(0.95)^t, detailing how it represents decay over time with a 5% decay rate per period. Learn the formula A(1 - r)^t, where A is the initial quantity, r is the decay rate, and t is time. Suitable for students in Grades 10-12.

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