Question

The temperature in the morning was -2 degrees. The temperature is dropping at a constant rate, and 4 hours later the temperature is now -22 degrees. How many degrees did the temperature change each hour?

Answer 1

Given:

Temperature in the morning = -2 degrees.

Temperature is dropping at a constant rate.

Temperature after 4 hours = -22 degrees.

To find:

The rate of change of temperature.

Solution:

Let y be the temperature after x hours from the morning.

Temperature in the morning is -2 degrees. It means, the ordered pair is (0,-2).

4 hours later the temperature is now -22 degrees. It means, the ordered pair is (4,-22).

Now, formula for average rate of change or slope is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{-22-(-2)}{4-0}$

$m=\dfrac{-22+2}{4}$

$m=\dfrac{-20}{4}$

$m=-5$

Therefore, the change in temperature is -5 per hour. It means the permutate is decreasing by 5 degrees per hour.