A researcher is cooling a metal. She cools the metal so that the temperature of the metal drops at a constant rate. After 13 minutes of cooling, the metal is 339°C. After 25 minutes, the metal is 135°C.(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.Thetemperatureofthemetaldecreasesatarateof°Cperminute. As time increases, the temperature of the metal increases.Thetemperatureofthemetalincreasesatarateof°Cperminute. (b)What was the temperature of the metal when the researcher started cooling it?°C
Question
A researcher is cooling a metal. She cools the metal so that the temperature of the metal drops at a constant rate. After 13 minutes of cooling, the metal is 339°C. After 25 minutes, the metal is 135°C.(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.Thetemperatureofthemetaldecreasesatarateof°Cperminute. As time increases, the temperature of the metal increases.Thetemperatureofthemetalincreasesatarateof°Cperminute. (b)What was the temperature of the metal when the researcher started cooling it?°C
Solution
(a) As time increases, the temperature of the metal decreases. The temperature of the metal decreases at a rate of __°C per minute.
To find the rate of decrease, we subtract the final temperature from the initial temperature and divide by the time difference.
So, (339°C - 135°C) / (25 min - 13 min) = 204°C / 12 min = 17°C per minute.
So, the temperature of the metal decreases at a rate of 17°C per minute.
(b) To find the initial temperature of the metal, we can use the rate of decrease and the temperature at a known time.
We know that after 13 minutes, the temperature was 339°C. So, the initial temperature would be the temperature after 13 minutes plus the amount of decrease in those 13 minutes.
So, 339°C + (13 min * 17°C/min) = 339°C + 221°C = 560°C.
So, the temperature of the metal when the researcher started cooling it was 560°C.
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