Complete the following table (in thousands of dollars per year). (Round your answers to three decimal places.)
h	1	0.1	0.01	0.001	0.0001
Avg. Rate of Change of P over [10, 10 + h]	  
Correct: Your answer is correct.

  

What do the results suggest about the rate of change of the median home price (in dollars) at the very beginning of 2020? [Hint: See Example 4.] (Round your answer to the nearest whole number.)
Home prices were increasing at a rate of about $   
 per year at the very beginning of 2020.

To solve this problem, we need more context on the function or data describing the median home prices, which isn't provided in the question. Typically, the average rate of change of a function $ P(t) $ over an interval $[10, 10 + h]$ (where 10 represents the year 2020) can be calculated using the formula for the difference quotient:

\[
\text{Average Rate of Change} = \frac{P(10 + h) - P(10)}{h}
\]

This formula gives the rate of change of $ P $ over the interval.

### Procedure:
1. We would first need the function or data values for $ P(t) $ at $ t = 10 $ (beginning of 2020) and $ P(10 + h) $ for different values of $ h $.
2. We then compute the average rate of change for each $ h $.
3. As $ h $ becomes smaller (approaching 0), the rate of change converges to the instantaneous rate of change at $ t = 10 $, which gives us the rate of change of the median home price at the very beginning of 2020.

If you have the function $ P(t) $ or the median home price data for 2020, please share it so I can calculate the values and complete the table. 

Do you have any questions or further details on the data?

---

Here are 5 questions to expand on this:
1. What is the function $ P(t) $ for the median home price?
2. Do you have the values of $ P(10 + h) $ for the different values of $ h $?
3. Would you like to understand more about how average rate of change relates to derivatives?
4. How does the value of $ h $ approaching 0 relate to instantaneous rates of change?
5. Do you have any specific values for home prices that need to be plugged into the equation?

**Tip:** The average rate of change formula is the foundation for understanding derivatives and instantaneous rates of change.

Complete the following table (in thousands of dollars per year). (Round your answers to three decimal places.) h 1 0.1 0.01 0.001 0.0001 Avg. Rate of Change of P over [10, 10 + h]. What do the results suggest about the rate of change of the median home price (in dollars) at the very beginning of 2020? Home prices were increasing at a rate of about $ ___ per year at the very beginning of 2020.

Learn how to calculate the rate of change of median home prices at the very beginning of 2020 using the difference quotient formula. Explore calculus concepts like the average rate of change and the derivative. Suitable for college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation