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

ryan 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.\n\n(a) find the average rate of change for the temperature from 0 minutes to 15 minutes.\n( square )°c per minute\n(b) find the average rate of change for the temperature from 60 minutes to 75 minutes.\n( -3.4 )°c per minute

ryan 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.\n\n(a) find the average rate of change for the temperature from 0 minutes to 15 minutes.\n( square )°c per minute\n(b) find the average rate of change for the temperature from 60 minutes to 75 minutes.\n( -3.4 )°c per minute

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for 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: Solve part (a)

For part (a), (x_1 = 0), (f(x_1)=193.5), (x_2 = 15), (f(x_2)=166.5). Substitute into the formula: (\frac{166.5 - 193.5}{15-0}=\frac{- 27}{15}=-1.8)

Step3: Solve part (b)

For part (b), (x_1 = 60), (f(x_1)=73.5), (x_2 = 75), (f(x_2)=22.5). Substitute into the formula: (\frac{22.5 - 73.5}{75 - 60}=\frac{-51}{15}=-3.4)

Answer:

(a) (-1.8)°C per minute; (b) (-3.4)°C per minute