Question

ms. valdezs science class is investigating newtons law of cooling. valerias group starts with 150ml of boiling water. they measure the temperature of the water every minute for 20 minutes. the table below shows their data. what was the average rate at which the temperature changed between minute 0 and minute 5? what was the average rate at which the temperature changed between minute 15 to minute 20? what do these average rates of change tell you about how water cools over time? enter your response in the space below. use the insert math button in the toolbar to help you type mathematical symbols and notation as needed. press alt+f10 (windows) or option-fn-f10 (mac) to navigate to the toolbar with your keyboard.

Explanation:

Step1: Calculate average rate of change formula

The formula for average rate of change is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: For minute 0 to minute 5

Here, $x_1 = 0,y_1=100,x_2 = 5,y_2 = 70$.
$\frac{70 - 100}{5-0}=\frac{- 30}{5}=-6$.

Step3: For minute 15 to minute 20

Here, $x_1 = 15,y_1 = 50,x_2=20,y_2 = 45$.
$\frac{45 - 50}{20 - 15}=\frac{-5}{5}=-1$.

Answer:

The average rate of change from minute 0 to minute 5 is $-6^{\circ}C$ per minute. The average rate of change from minute 15 to minute 20 is $-1^{\circ}C$ per minute. These average rates of change tell us that the water cools at a faster rate in the initial minutes (0 - 5) compared to the later minutes (15 - 20).