Question

during a study, the temperature, in degrees celsius (°c), of the air in a chamber was recorded to the nearest integer at certain times. the scatter - plot shows the recorded temperature y, in °c, of the air in the chamber x minutes after the start of the study. what was the average rate of change, in °c per minute, of the recorded temperature of the air in the chamber from x = 5 to x = 7?

Explanation:

Step1: Recall average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 5$, $b = 7$. We need to find the $y$-values corresponding to $x = 5$ and $x = 7$ from the scatter - plot.

Step2: Identify $y$-values from the scatter - plot

From the scatter - plot, when $x = 5$, $y_1=15$ (approximate the $y$-value at $x = 5$), and when $x = 7$, $y_2 = 24$ (approximate the $y$-value at $x = 7$).

Step3: Calculate the average rate of change

Substitute $a = 5$, $b = 7$, $y_1=15$, and $y_2 = 24$ into the formula $\frac{y_2 - y_1}{b - a}=\frac{24 - 15}{7 - 5}=\frac{9}{2}=4.5$.

Answer:

$4.5$