The function f, of, t, equals, 4300, left parenthesis, 0, point, 9, 6, right parenthesis, start superscript, 24, t, end superscriptf(t)=4300(0.96) 
24t
  represents the change in a quantity over t days. What does the constant 0.96 reveal about the rate of change of the quantity?
Answer
Attempt 1 out of 2

The function is  exponentially at a rate of % every .

In the given function \( f(t) = 4300(0.96)^{24t} \), the constant \( 0.96 \) reveals important information about the rate of change of the quantity over time.

### Analysis:
- The base of the exponential, \( 0.96 \), represents the **rate of decay** in this case. Since it is less than 1, the quantity decreases over time.
- Specifically, \( 0.96 \) indicates that the quantity decreases by **4%** (since \( 1 - 0.96 = 0.04 \), or 4%) for each time period being measured. 
- Therefore, the quantity is decreasing at a rate of **4% every day**.

### Final Interpretation:
The constant \( 0.96 \) reveals that the quantity is decaying at a rate of **4% per unit of time**, where the time period is determined by the factor \( 24t \) (for every time period of \( t \) days).

Would you like more details or have any questions?

Here are 5 related questions to further explore:

1. What does the initial value of 4300 in the function represent?
2. How would the rate of decay change if the constant was 0.97 instead of 0.96?
3. Can you determine the half-life of the quantity based on the given function?
4. How does changing the exponent \( 24t \) affect the behavior of the function?
5. What would happen to the function if the base was greater than 1?

**Tip**: When the base of an exponential function is less than 1, it always indicates exponential decay.

The function f(t) = 4300(0.96)^{24t} represents the change in a quantity over t days. What does the constant 0.96 reveal about the rate of change of the quantity?

Explore the exponential decay function f(t) = 4300(0.96)^{24t} and learn how the constant 0.96 indicates a 4% daily decrease. This problem highlights key concepts in exponential decay and is ideal for students in Grades 9-12.

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