To analyze the exponential function provided:

$y = 4600 \times (0.96)^x$

Step 1: Identify Growth or Decay

In an exponential function of the form $y = a \times b^x$, if $b$ (the base of the exponent) is:

• Greater than 1, the function represents exponential growth.
• Between 0 and 1, the function represents exponential decay.

Here, $b = 0.96$, which is less than 1, indicating that this is an exponential decay function.

Step 2: Determine the Percentage Rate of Decrease

The percentage rate of change can be calculated as follows:

1. Subtract $b$ from 1: $1 - 0.96 = 0.04$.
2. Convert this to a percentage: $0.04 \times 100\% = 4\%$.

Conclusion

This function represents an exponential decay with a percentage rate of decrease of 4%.

Would you like further details or have any questions?

Here are some additional related questions for further exploration:

1. How would the equation change if it represented a 6% decay?
2. What is the significance of the initial value, 4600, in the context of this equation?
3. How does the decay rate affect the speed at which the function approaches zero?
4. What would the equation look like for a 4% growth instead of decay?
5. How can you graph this function to visually observe the decay?

Tip: When identifying growth or decay, always check the base of the exponent. Values below 1 indicate decay, while values above 1 indicate growth.