justin is cooking a roast. the table below gives the temperature r(t) of the roast (in degrees celsius), at…

justin is cooking a roast. the table below gives the temperature r(t) of the roast (in degrees celsius), at a few times t (in minutes) after he removed it from the oven. time t (minutes) temperature r(t) (°c) 0 226.6 10 205.6 30 157.6 50 119.6 70 61.6 (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 50 minutes to 70 minutes. °c per minute

justin is cooking a roast. the table below gives the temperature r(t) of the roast (in degrees celsius), at a few times t (in minutes) after he removed it from the oven. time t (minutes) temperature r(t) (°c) 0 226.6 10 205.6 30 157.6 50 119.6 70 61.6 (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 50 minutes to 70 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 $t = 30$, $a = 0$, $b = 30$, $R(0)=226.6$ and $R(30)=157.6$. The average rate of change is $\frac{R(30)-R(0)}{30 - 0}=\frac{157.6 - 226.6}{30}=\frac{-69}{30}=-2.3$.

Step3: Calculate average rate of change for part (b)

For the time interval from $t = 50$ to $t = 70$, $a = 50$, $b = 70$, $R(50)=119.6$ and $R(70)=61.6$. The average rate of change is $\frac{R(70)-R(50)}{70 - 50}=\frac{61.6 - 119.6}{20}=\frac{-58}{20}=-2.9$.

Answer:

(a) $-2.3$ (b) $-2.9$