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?
To find the rate of change from the given table, we need to calculate the slope, which represents how much the snowfall amount changes per hour. The table provided lists the snowfall amounts for different lengths of snowfall time.
Here's the step-by-step process to find the rate of change:
1. Identify the pairs of corresponding values for length of snowfall (in hours) and amount of snow on the ground (in inches).
2. Use the slope formula [tex]\( \text{slope} = \frac{\Delta y}{\Delta x} \)[/tex], where [tex]\( \Delta y \)[/tex] is the change in the snowfall amount and [tex]\( \Delta x \)[/tex] is the change in the length of snowfall.
Let's calculate the rate of change between each successive pair: - Between 0 and 0.5 hours: [tex]\[
\text{Slope} = \frac{4.5 - 3.3}{0.5 - 0} = \frac{1.2}{0.5} = 2.4 \text{ inches per hour}
\][/tex]
- Between 0.5 and 1.0 hours: [tex]\[
\text{Slope} = \frac{5.7 - 4.5}{1.0 - 0.5} = \frac{1.2}{0.5} = 2.4 \text{ inches per hour}
\][/tex]
- Between 1.0 and 1.5 hours: [tex]\[
\text{Slope} = \frac{6.9 - 5.7}{1.5 - 1.0} = \frac{1.2}{0.5} = 2.4 \text{ inches per hour}
\][/tex]
- Between 1.5 and 2.0 hours: [tex]\[
\text{Slope} = \frac{8.1 - 6.9}{2.0 - 1.5} = \frac{1.2}{0.5} = 2.4 \text{ inches per hour}
\][/tex]
As we can see, the rate of change (slope) is the same for all pairs—it is [tex]\( 2.4 \)[/tex] inches per hour.
Thus, the rate of change for the snowfall amount is: [tex]\[ \boxed{2.4} \][/tex] inches per hour.
