Question

Jose Is cooking a roast. The table below gives the temperature (1) of the roast (In degrees Celsius), at a few timest (In minutes) after he removed it from theoven.Timet Temperature R (1)(minutes)(c)010305070226.6205.6157.6119.661.6(a) Find the average rate of change for the temperaturefrom 0 minutes to 10 minutes.0 °C per minute(b) Find the average rate of change for the temperaturefrom 30 minutes to 50 minutes.[ °C per minute

Answer 1

(a). From the given table,

R(0)=226.6

R(10)=205.6

The average rate of change for the temperature from 0 minutes to 10 minutes is

`\begin{gathered} A=(R(10)-R(0))/(10-0) \\ =(205.6-226.6)/(10) \\ =-2.1 \end{gathered}`

(a) The average rate of change for the temperature from 0 minutes to 10 minutes is -2.1 (in degree centrigrade)

Minus sign implies that the temperature is deacreasing with increasing time

(b). Again,

R(30)=157.6

R(50)=119.6

The average rate of change for the temperature from 30 minutes to 50 minutes is

`\begin{gathered} A=(R(50)-R(30))/(50-30) \\ =(119.6-157.6)/(20) \\ =-1.9 \end{gathered}`

(b) The average rate of change for the temperature from 30 minutes to 50 minutes is -1.9 (in degree centrigrade)

Minus sign implies that the temperature is deacreasing with increasing time