7 firing a piece of pottery in a kiln takes p...
7 firing a piece of pottery in a kiln takes place at different temperatures for different amounts of time. the graph below shows the temperatures in a kiln while firing a piece of pottery after the kiln is preheated to 200°f. during which time interval did the temperature in the kiln show the greatest average rate of change? 1) 0 to 1 hour 2) 1 hour to 1.5 hours 3) 2.5 hours to 5 hours 4) 5 hours to 8 hours
Answer
# Explanation:
## Step1: Recall rate - of - change formula
The average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.
## Step2: Calculate rate of change for 0 to 1 hour
Let $x_1 = 0$, $y_1=200$, $x_2 = 1$, $y_2 = 700$. The rate of change is $\frac{700 - 200}{1-0}=\frac{500}{1}=500$ °F per hour.
## Step3: Calculate rate of change for 1 to 1.5 hours
Let $x_1 = 1$, $y_1 = 700$, $x_2 = 1.5$, $y_2 = 900$. The rate of change is $\frac{900 - 700}{1.5 - 1}=\frac{200}{0.5}=400$ °F per hour.
## Step4: Calculate rate of change for 2.5 to 5 hours
Let $x_1 = 2.5$, $y_1 = 1300$, $x_2 = 5$, $y_2 = 1640$. The rate of change is $\frac{1640 - 1300}{5 - 2.5}=\frac{340}{2.5}=136$ °F per hour.
## Step5: Calculate rate of change for 5 to 8 hours
Let $x_1 = 5$, $y_1 = 1640$, $x_2 = 8$, $y_2 = 1800$. The rate of change is $\frac{1800 - 1640}{8 - 5}=\frac{160}{3}\approx53.33$ °F per hour.
# Answer:
1) 0 to 1 hour