in 1998 Linda purchased a house for $144,000 in 2009. The house is worth $245,000. Find the average annual rate of change in the value of house.

To find the average annual rate of change in the value of Linda's house, we can use the formula for the average rate of change:

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

### Step-by-Step Solution:

1. **Determine the initial and final values:**

   - Initial value (in 1998): $ V_1 = 144,000 $ dollars
   - Final value (in 2009): $ V_2 = 245,000 $ dollars

2. **Determine the change in value:**

   \[
   \text{Change in Value} = V_2 - V_1 = 245,000 - 144,000 = 101,000 \text{ dollars}
   \]

3. **Determine the time period:**

   - Initial year: 1998
   - Final year: 2009

   \[
   \text{Change in Time} = 2009 - 1998 = 11 \text{ years}
   \]

4. **Calculate the average annual rate of change:**

   \[
   \text{Average Rate of Change} = \frac{101,000}{11} \approx 9,181.82 \text{ dollars per year}
   \]

### Conclusion:

The average annual rate of change in the value of Linda's house from 1998 to 2009 is **$9,181.82 per year**.

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

### Related Questions:
1. What would be the value of the house in 2015 if it continued to appreciate at the same rate?
2. How does the average rate of change compare to the compound annual growth rate?
3. What is the percentage increase in the value of the house from 1998 to 2009?
4. What would the house be worth in 2024 assuming the same average rate of change continues?
5. How can inflation affect the real rate of return on the house investment?

#### Tip:
When calculating the average rate of change, always ensure the time period is consistent with the units you want for the rate (e.g., per year, per month).

In 1998, Linda purchased a house for $144,000. In 2009, the house is worth $245,000. Find the average annual rate of change in the value of the house.

This problem involves calculating the average annual rate of change in the value of a house purchased for $144,000 in 1998 and valued at $245,000 in 2009. Learn how to apply the formula for average rate of change over an 11-year period to find a yearly growth rate of $9,181.82.

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