What is the average rate of change in population from 1900 to 1990 if it increased from 75 million to 250 million?

Average Rate of Change = (250 - 75) / (1990 - 1900) = 175 / 90 = 1.94 million people/year.

How do you interpret the average rate of change in a real-world context?

It represents how much a quantity changes on average for each unit of change in another quantity.

What is the average rate of change of a climber's altitude from 400 feet to 700 feet over 4 hours?

Average Rate of Change = (700 - 400) / (6 - 2) = 300 / 4 = 75 feet/hour.

If a rocket's altitude changes from 1.5 miles to 8 miles in 120 seconds, what is its average rate of change in miles per second?

Average Rate of Change = (8 - 1.5) / (120) = 6.5 / 120 = 0.054 mps.

What is the significance of the interval in calculating average rate of change?

The interval determines the specific range over which the change is measured, affecting the average rate.

How can average rate of change be applied in economics?

It can be used to analyze changes in revenue, costs, or profits over time.

What is the average rate of change of a function at a specific point?

It is the limit of the average rate of change as the interval approaches zero, known as the derivative.

Why is understanding average rate of change important in calculus?

It lays the foundation for understanding derivatives and instantaneous rates of change.

Average Rate of Change

Flashcard

•

Mathematics

•

9th Grade

•

Practice Problem

•

Hard

•

CCSS

8.F.B.4, HSF.IF.B.6

Standards-aligned

Wayground Content

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15 questions

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FLASHCARD QUESTION

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

How do you calculate the average rate of change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a), where [a, b] is the interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

What does a positive average rate of change indicate?

Back

A positive average rate of change indicates that the function is increasing over the interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

What does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

What is the average rate of change of a linear function?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

If a function has an average rate of change of 0, what does that mean?

Back

An average rate of change of 0 means that the function's value does not change over the interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

Example: Find the average rate of change from (2, 4) to (6, 10).

Back

Average Rate of Change = (10 - 4) / (6 - 2) = 6 / 4 = 1.5.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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