Average Rate of Change Assignment

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. It is calculated as \( \frac{f(b) - f(a)}{b - a} \) where \( a \) and \( b \) are the endpoints of the interval.

Front

How do you calculate the average rate of change from a graph?

Back

To calculate the average rate of change from a graph, identify two points on the graph, \( (x_1, y_1) \) and \( (x_2, y_2) \). Use the formula \( \frac{y_2 - y_1}{x_2 - x_1} \) to find the average rate of change.

Front

What is the average rate of change of a function represented by a linear equation?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line, which can be calculated as \( \frac{\Delta y}{\Delta x} \).

Front

If a climber is at 400 feet after 2 hours and 700 feet after 6 hours, what is the average rate of change?

Back

The average rate of change is \( \frac{700 - 400}{6 - 2} = \frac{300}{4} = 75 \) feet per hour.

Front

What does a negative average rate of change indicate?

Back

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

Front

How do you find the average rate of change from a function?

Back

To find the average rate of change from a function \( f(x) \) over the interval \( [a, b] \), use the formula \( \frac{f(b) - f(a)}{b - a} \).

Front

What is the average rate of change of the price of gold from 2000 to 2022 if it was $279.29 in 2000 and $1868.8 in 2022?

Back

The average rate of change is \( \frac{1868.8 - 279.29}{2022 - 2000} = \frac{1589.51}{22} \approx 72 \) dollars per year.

Front

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

Back

The average rate of change of a quadratic function over an interval can be calculated using the same formula as for linear functions, but the value will vary depending on the specific points chosen.

Front

If a ball's height is given by \( h(t) = -2t^2 + 34 \), how do you find the average rate of change between 0 and 4 seconds?

Back

Calculate \( h(0) \) and \( h(4) \), then use the formula \( \frac{h(4) - h(0)}{4 - 0} \). The average rate of change is \( -8 \) meters per second.

Front

What is the average rate of change of a function that decreases from 600 gallons to 525 gallons over 5 minutes?

Back

The average rate of change is \( \frac{525 - 600}{5 - 0} = \frac{-75}{5} = -15 \) gallons per minute.