scott is cooking a roast. the table below gives the temperature r(t) of the roast (in degrees celsius), at a…
scott 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. (a) find the average rate of change for the temperature from 0 minutes to 10 minutes. (b) find the average rate of change for the temperature from 30 minutes to 70 minutes.
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 $t = 10$, $a = 0$, $b = 10$, $R(0)=226.6$ and $R(10)=205.6$. The average rate of change is $\frac{R(10)-R(0)}{10 - 0}=\frac{205.6 - 226.6}{10}=\frac{- 21}{10}=-2.1$.
Step3: Calculate average rate of change for part (b)
For the time interval from $t = 30$ to $t = 70$, $a = 30$, $b = 70$, $R(30)=157.6$ and $R(70)=61.6$. The average rate of change is $\frac{R(70)-R(30)}{70 - 30}=\frac{61.6-157.6}{40}=\frac{-96}{40}=-2.4$.
Answer:
(a) $-2.1$ (b) $-2.4$