milan is cooking a roast. the table below gives the temperature r(t) of the from the oven. time t (minutes)…
milan is cooking a roast. the table below gives the temperature r(t) of the from the oven. time t (minutes) temperature r(t) (°c) 0 193.5 15 166.5 30 130.5 60 73.5 75 22.5 (a) find the average rate of change for the temperature from 0 minutes to 30 minutes. °c per minute (b) find the average rate of change for the temperature from 60 minutes to 75 minutes. °c per minute
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$.
Step2: Calculate average rate of change for part (a)
For the time interval from $t = 0$ to $t = 30$, $a = 0$, $b = 30$, $R(0)=193.5$ and $R(30)=130.5$. The average rate of change is $\frac{R(30)-R(0)}{30 - 0}=\frac{130.5 - 193.5}{30}=\frac{- 63}{30}=-2.1$.
Step3: Calculate average rate of change for part (b)
For the time interval from $t = 60$ to $t = 75$, $a = 60$, $b = 75$, $R(60)=73.5$ and $R(75)=22.5$. The average rate of change is $\frac{R(75)-R(60)}{75 - 60}=\frac{22.5 - 73.5}{15}=\frac{-51}{15}=-3.4$.
Answer:
(a) $-2.1$ (b) $-3.4$