Week 4 - Average Rate of Change

Front

What is the average rate of change?

Back

The average rate of change is a measure of how much a quantity changes, on average, over a specific interval. It is calculated as the change in the value of a function divided by the change in the input value.

Front

How do you calculate the average rate of change?

Back

To calculate the average rate of change between two points (x1, y1) and (x2, y2), use the formula: (y2 - y1) / (x2 - x1).

Front

What is the average rate of change from 0 to 2 seconds if the distance changes from 0 to 5 feet?

Back

2.5 feet per second.

Front

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

Back

75 feet per hour.

Front

What does a negative average rate of change indicate?

Back

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

Front

Calculate the average rate of change from 20 to 40 minutes if the gallons of fuel change from 10 to 0.

Back

-2 gallons per minute.

Front

What is the significance of the average rate of change in real-world applications?

Back

The average rate of change helps to understand trends and behaviors in various contexts, such as speed, growth, and decay.

Front

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

Back

0.055 miles per second.

Front

What is the average rate of change if the function values are 10 and 30 over the interval from 1 to 3?

Back

10 units per interval.

Front

Define 'interval' in the context of average rate of change.

Back

An interval is the range of input values (x-values) over which the average rate of change is calculated.