brian is cooking a roast. the table below gives the temperature r(t) of the roast (in degrees celsius), at a…
brian 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) 0 193.5 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 15 minutes. °c per minute (b) find the average rate of change for the temperature from 30 minutes to 75 minutes. °c per minute
Answer
Explanation:
Step1: Fórmula de tasa de cambio promedio
La tasa de cambio promedio de una función $y = f(x)$ en el intervalo $[x_1,x_2]$ es $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.
Step2: Resolver (a)
Para el intervalo de $t_1 = 0$ a $t_2=15$, $R(t_1)=193.5$ y $R(t_2) = 166.5$. $\frac{R(15)-R(0)}{15 - 0}=\frac{166.5 - 193.5}{15}=\frac{- 27}{15}=-1.8$
Step3: Resolver (b)
Para el intervalo de $t_1 = 30$ a $t_2 = 75$, $R(t_1)=130.5$ y $R(t_2)=22.5$. $\frac{R(75)-R(30)}{75 - 30}=\frac{22.5-130.5}{45}=\frac{-108}{45}=- 2.4$
Answer:
(a) $-1.8$ (b) $-2.4$