The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. What is the rate of change?
| Length of Snowfall (hours) | Amount of Snow on the Ground (inches) |
| :------------------------- | :------------------------------------- |
| 0 | 3.3 |
| 0.5 | 4.5 |
| 1.0 | 5.7 |
| 1.5 | 6.9 |
| 2.0 | 8.1 |
A. 1.2 inches per hour
B. 2.4 inches per hour
C. 3.3 inches per hour
D. 5.7 inches per hour
Answer (2)
Identify that the problem asks for the rate of change of a linear function.
Use the formula for rate of change (slope): r a t e = x 2 − x 1 y 2 − y 1 .
Substitute two points from the table into the formula: r a t e = 0.5 − 0 4.5 − 3.3 .
Calculate the rate of change: r a t e = 2.4 inches per hour. The final answer is 2.4 inches per hour .
Explanation
Understanding the Problem We are given a table of values representing a linear function that shows the amount of snow on the ground (in inches) at different times (in hours) since a snowstorm began. We need to find the rate of change of this linear function, which represents how much the amount of snow on the ground increases per hour.
Setting up the Calculation The rate of change of a linear function is also known as its slope. We can calculate the slope using any two points from the table. Let's use the points (0, 3.3) and (0.5, 4.5). The formula for the slope (rate of change) is: r a t e = c han g e in t im e c han g e in s n o w am o u n t = x 2 − x 1 y 2 − y 1
Substituting the Values Now, we substitute the values from the chosen points into the formula: r a t e = 0.5 − 0 4.5 − 3.3
Calculating the Rate of Change Next, we simplify the expression: r a t e = 0.5 1.2 = 2.4 So, the rate of change is 2.4 inches per hour.
Final Answer The rate of change of the snow fall is 2.4 inches per hour.
Examples
Understanding rates of change is crucial in many real-world scenarios. For instance, if you're tracking the speed of a car, the rate of change tells you how quickly the car's velocity is changing. Similarly, in finance, the rate of change can represent the growth rate of an investment. In our case, knowing the rate of snowfall helps in planning activities like snow removal or predicting potential travel disruptions. The concept of rate of change allows us to quantify and understand dynamic processes around us, making it a fundamental tool in various fields.
The rate of change of the snow amount over time is determined using the slope formula, resulting in a rate of 2.4 inches per hour. Therefore, the correct answer is B. 2.4 inches per hour.
;
