To solve this problem:

Step 1: Identify Growth or Decay

The general form of an exponential function is:

$y = a \cdot b^x$

Where:

• $a$ is the initial amount,
• $b$ is the base of the exponential growth/decay,
• $b > 1$: Growth,
• $0 < b < 1$: Decay.

In the given equation $y = 99 \cdot (1.04)^x$, the base $b = 1.04$, which is greater than 1. Therefore, the function represents growth.

Step 2: Determine the Percentage Rate

The percentage rate of growth is determined by subtracting 1 from the base $b$, and then converting the result to a percentage:

$\text{Rate of growth} = (b - 1) \cdot 100$

Substituting $b = 1.04$:

$\text{Rate of growth} = (1.04 - 1) \cdot 100 = 0.04 \cdot 100 = 4\%$

Final Answer:

• The change represents growth.
• The percentage rate of increase is 4%.

Would you like me to explain further or provide more examples?

Here are 5 related questions to explore:

1. How does the base of an exponential function affect growth or decay?
2. What happens to the graph of an exponential function as $x$ increases or decreases?
3. How would the equation change if it represented decay instead of growth?
4. Can you identify real-life examples of exponential growth or decay?
5. How do you calculate the growth/decay rate from a different base?

Tip: Always check the base of the exponential function carefully to identify whether it's greater or less than 1—it determines the type of change!