this table displays the height of a balloon as it floats away. what is the rate of change for the height as…

this table displays the height of a balloon as it floats away. what is the rate of change for the height as the time increases by 1 minute?\n| time (min) | height (ft) |\n| ---- | ---- |\n| 10 | 64 |\n| 11 | 73.5 |\n| 12 | 83 |\n| 13 | 92.5 |\n| 14 | 102 |\n| 15 | 111.5 |\nrate of change =

this table displays the height of a balloon as it floats away. what is the rate of change for the height as the time increases by 1 minute?\n| time (min) | height (ft) |\n| ---- | ---- |\n| 10 | 64 |\n| 11 | 73.5 |\n| 12 | 83 |\n| 13 | 92.5 |\n| 14 | 102 |\n| 15 | 111.5 |\nrate of change =

Answer

Explanation:

Step1: Recall rate - of - change formula

The rate of change formula is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x$ is time (in minutes) and $y$ is height (in feet). We can take any two - consecutive data points. Let's take $(x_1,y_1)=(10,64)$ and $(x_2,y_2)=(11,73.5)$.

Step2: Calculate the rate of change

$\frac{y_2 - y_1}{x_2 - x_1}=\frac{73.5 - 64}{11 - 10}=\frac{9.5}{1}=9.5$. We can check with other consecutive points. For example, if we take $(x_1,y_1)=(11,73.5)$ and $(x_2,y_2)=(12,83)$, then $\frac{y_2 - y_1}{x_2 - x_1}=\frac{83 - 73.5}{12 - 11}=\frac{9.5}{1}=9.5$.

Answer:

$9.5$