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 initial value in a payment scenario?

Back

The initial value is the amount paid at the beginning of a transaction or the starting point of a function.

Front

In Tim's phone payment scenario, what is the initial value?

Back

$125, which is the amount paid on the day of purchase.

Front

What is the rate of change in a payment scenario?

Back

The rate of change is the amount that a quantity increases or decreases per unit of time or per unit of another variable.

Front

In Tim's phone payment scenario, what is the rate of change?

Back

$50 per month, which is the amount Tim pays each month after the initial payment.

Front

What does a negative Average Rate of Change indicate?

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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 quantity changes from 10 to 0 gallons.

Back

The Average Rate of Change is (0 - 10) / (40 - 20) = -0.5 gallons per minute.

Front

What is the Average Rate of Change from 0 to 2 seconds if the distance changes from 0 to 5 feet?

Back

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

Front

What is the significance of the Average Rate of Change in real-life scenarios?

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The Average Rate of Change helps to understand trends, make predictions, and analyze the behavior of quantities over time.