Susan's Elevation At The Top Of A Mountain Is 1,530 Meters. After 4 Hours Of Climbing Down, Her Elevation Is 680 Meters.What Is Susan's Average Change In Elevation, In Meters Per Hour?A. $-850$B. $-382.50$C. $-212.5$D.

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Understanding the Problem

Susan's elevation at the top of a mountain is 1,530 meters. After 4 hours of climbing down, her elevation is 680 meters. We need to find Susan's average change in elevation, in meters per hour.

Step 1: Calculate the Change in Elevation

To find the average change in elevation, we first need to calculate the total change in elevation. This can be done by subtracting the final elevation from the initial elevation.

Change in elevation = Initial elevation - Final elevation
Change in elevation = 1530 - 680
Change in elevation = 850

Step 2: Calculate the Average Change in Elevation

Now that we have the total change in elevation, we can calculate the average change in elevation by dividing the total change in elevation by the time taken.

Average change in elevation = Change in elevation / Time taken
Average change in elevation = 850 / 4
Average change in elevation = -212.5

Conclusion

The average change in elevation is -212.5 meters per hour.

Answer

The correct answer is C. $-212.5$.

Discussion

This problem requires us to understand the concept of average rate of change and how to apply it to real-world scenarios. The average rate of change is calculated by dividing the total change in elevation by the time taken. In this case, the total change in elevation is 850 meters, and the time taken is 4 hours. Therefore, the average change in elevation is -212.5 meters per hour.

Real-World Applications

Understanding the concept of average rate of change has many real-world applications. For example, in finance, it can be used to calculate the average rate of return on investment. In physics, it can be used to calculate the average velocity of an object. In this case, it can be used to calculate the average change in elevation of an object.

Tips and Tricks

When solving problems involving average rate of change, make sure to:

  • Calculate the total change in the variable (in this case, elevation)
  • Divide the total change by the time taken
  • Check the units of the answer to ensure they match the units of the variable

Q: What is average rate of change?

A: The average rate of change is a measure of how much a variable changes over a given period of time. It is calculated by dividing the total change in the variable by the time taken.

Q: How do I calculate the average rate of change?

A: To calculate the average rate of change, follow these steps:

  1. Calculate the total change in the variable.
  2. Divide the total change by the time taken.

Q: What is the formula for average rate of change?

A: The formula for average rate of change is:

Average rate of change = Total change / Time taken

Q: What are some real-world applications of average rate of change?

A: Average rate of change has many real-world applications, including:

  • Finance: calculating the average rate of return on investment
  • Physics: calculating the average velocity of an object
  • Engineering: calculating the average rate of change of a system's parameters
  • Economics: calculating the average rate of change of a country's GDP

Q: What are some common mistakes to avoid when calculating average rate of change?

A: Some common mistakes to avoid when calculating average rate of change include:

  • Failing to calculate the total change in the variable
  • Failing to divide the total change by the time taken
  • Using the wrong units for the answer
  • Failing to check the units of the answer

Q: How do I check the units of the answer?

A: To check the units of the answer, make sure that the units of the answer match the units of the variable. For example, if the variable is elevation in meters, the units of the answer should also be meters per hour.

Q: What is the difference between average rate of change and instantaneous rate of change?

A: The average rate of change is a measure of how much a variable changes over a given period of time, while the instantaneous rate of change is a measure of how much a variable changes at a specific point in time.

Q: How do I calculate the instantaneous rate of change?

A: To calculate the instantaneous rate of change, you need to use calculus and find the derivative of the function.

Q: What are some common applications of instantaneous rate of change?

A: Some common applications of instantaneous rate of change include:

  • Physics: calculating the instantaneous velocity of an object
  • Engineering: calculating the instantaneous rate of change of a system's parameters
  • Economics: calculating the instantaneous rate of change of a country's GDP

Conclusion

Average rate of change is an important concept in mathematics that has many real-world applications. By understanding how to calculate the average rate of change, you can solve problems in finance, physics, engineering, and economics. Remember to check the units of the answer and avoid common mistakes when calculating the average rate of change.