A researcher is cooling a metal. She cools the metal so that the temperature of the metal drops at a constant rate. After 14 minutes of cooling, the metal is 326c. After 27 minutes, the metal is 118c.
(a)Choose the statement that best describes how the time and the temperature of the metal are related. Then fill in the blank.
As time increases, the temperature of the metal decreases.
As time increases, the temperature of the metal increases.
(b)What was the temperature of the metal when the researcher started cooling it?
To determine the temperature of the metal when the researcher started cooling it, we can create a linear equation using the given information.
Let's use the coordinates (t, T) to represent time and temperature respectively. We have two points on the line: (14, 326) and (27, 118).
Using the slope formula:
slope = (T2 - T1) / (t2 - t1)
slope = (118 - 326) / (27 - 14)
slope = -208 / 13
slope = -16
Using the point-slope form of a linear equation:
T - T1 = m(t - t1)
T - 326 = -16(t - 14)
T - 326 = -16t + 224
T = -16t + 550
Now, let's substitute t with 0 (when the researcher started cooling it):
T = -16(0) + 550
T = 550
Therefore, the temperature of the metal when the researcher started cooling it was 550°C.