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Enrollment in a school has grown exponentially since the school opened. A graph depicting this growth is shown. Determine the percentage rate of growth. 

To determine the percentage rate of growth from the graph, we can follow these steps:

1. **Identify two points on the graph:** We need to find two points (time, enrollments) that lie on the curve. From the graph, we can approximate these points.

2. **Set up the exponential growth formula:** The formula for exponential growth is:
   \[
   N(t) = N_0 \cdot e^{rt}
   \]
   Where:
   - \(N(t)\) is the number of enrollments at time \(t\).
   - \(N_0\) is the initial number of enrollments.
   - \(r\) is the growth rate.
   - \(t\) is the time.

3. **Calculate the growth rate:** By using the two points and solving for \(r\), we can determine the percentage rate of growth.

### Step 1: Identify Two Points

From the graph:
- At \(t = 0\), \(N(0) \approx 10\) (initial enrollment).
- At \(t = 30\), \(N(30) \approx 120\).

### Step 2: Use the Exponential Growth Formula

Using the exponential growth formula:
\[
120 = 10 \cdot e^{30r}
\]

### Step 3: Solve for \(r\)

To find the growth rate \(r\), let's solve the equation:

\[
\frac{120}{10} = e^{30r}
\]

\[
12 = e^{30r}
\]

Taking the natural logarithm on both sides:

\[
\ln(12) = 30r
\]

Now, let's calculate \(r\).The percentage rate of growth is approximately **8.28%** per year.

Would you like further details on this calculation or have any additional questions?

Here are 5 related questions you might find interesting:
1. How would the growth rate change if the initial enrollment was different?
2. How can you use this growth rate to predict future enrollments?
3. What would the enrollment be after 40 years at this growth rate?
4. How would the graph change if the growth rate were doubled?
5. What are some real-world factors that could affect this growth rate?

**Tip:** When working with exponential growth, small changes in the rate can lead to significant differences over time due to the compounding effect.

Learn how to calculate the percentage rate of growth from an exponential growth graph with detailed steps and examples. Understand the exponential growth formula and how to apply it to determine growth rates. Suitable for high school students and anyone interested in exponential growth calculations.

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