The given equation is \( y = 4(0.95)^x \), which represents an exponential decay function. The general form of an exponential decay function is:

\[
y = a(1 - r)^x
\]

Where:
- \( a \) is the initial value (in this case, \( 4 \)),
- \( r \) is the decay rate,
- \( (1 - r) \) is the decay factor (here, \( 0.95 \)),
- \( x \) is the independent variable.

From the equation, we can identify the decay factor as \( 0.95 \), which means \( 1 - r = 0.95 \). Solving for \( r \):

\[
1 - r = 0.95
\]
\[
r = 1 - 0.95 = 0.05
\]

Thus, the decay rate is **5%**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the initial value of the function?
2. How would the graph of the function change if the decay rate increased?
3. What is the half-life of the function?
4. How does the decay factor relate to the decay rate?
5. How does the function behave as \( x \) approaches infinity?

**Tip:** The decay rate represents the percentage decrease per unit of time or input (in this case, per \( x \)).

What is the decay rate for y = 4(0.95)^x?

Understand how to find the decay rate for the exponential function y = 4(0.95)^x. This step-by-step solution explains the exponential decay formula, how to identify the decay factor, and solve for the decay rate. Suitable for students in Grades 9-12.

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