Week 4 - Average Rate of Change

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.

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.

Front

What does a positive average rate of change indicate?

Back

It indicates that the function is increasing over the interval.

Front

What does a negative average rate of change indicate?

Back

It indicates that the function is decreasing over the interval.

Front

What is the average rate of change from x=0 to x=1 if f(0)=0 and f(1)=3?

Back

Average Rate of Change = (3 - 0) / (1 - 0) = 3.

Front

If a population grows from 1 million to 2 million over 10 years, what is the average rate of change?

Back

Average Rate of Change = (2 million - 1 million) / (10 years) = 0.1 million people/year.

Front

What is the average rate of change in Mrs. Gordon's speed from 0 to 2 seconds if she travels 5 feet?

Back

Average Rate of Change = (5 feet - 0 feet) / (2 seconds - 0 seconds) = 2.5 feet per second.

Front

Which interval has the largest average rate of change: 13 to 14, 13 to 17, 16 to 17, or 16 to 19?

Back

The interval 16 to 17 has the largest average rate of change.

Front

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

Back

It represents how much a quantity changes on average per unit of time or distance.

Front

What is the average rate of change for a climber who goes from 400 feet to 700 feet in 4 hours?

Back

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