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To find Karen's average rate of change in height per year between the ages of 12 and 20, we use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{\text{Change in Height}}{\text{Change in Time}}
\]

From the problem statement, Karen's height at 12 years old was 48 inches, and at 20 years old, it was 64 inches. Thus, the change in height is:

\[
\text{Change in Height} = 64 \text{ inches} - 48 \text{ inches} = 16 \text{ inches}
\]

The change in time (age) from 12 years to 20 years is:

\[
\text{Change in Time} = 20 \text{ years} - 12 \text{ years} = 8 \text{ years}
\]

Now, calculating the average rate of change:

\[
\text{Average Rate of Change} = \frac{16 \text{ inches}}{8 \text{ years}} = 2 \text{ inches per year}
\]

Karen's height increased, and her average rate of change in height per year over this period was 2 inches per year.

Would you like more details or have any questions? Here are some related topics we could explore:

1. How do these calculations relate to slopes of lines in coordinate geometry?
2. What would be the implications if the rate of change was not constant over the years?
3. How to graph this change in height over time?
4. How to calculate the total increase in height over a different age range?
5. What are some real-world applications of average rate of change outside of growth in height?

**Tip:** When analyzing any function or data for changes over time, finding the average rate of change gives a simplified view of the behavior between any two points. This is a fundamental concept in both mathematics and many applied sciences.

When Karen was 12 years old, she was 48 inches tall. By the time she was 20 years old, she was 64 inches tall. Find her average rate of change per year.

Learn how to calculate the average rate of change in height over time with this example where Karen's height increased from 48 inches at age 12 to 64 inches at age 20. Suitable for middle school students (Grades 6-8).

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