Fill in the blanks

Question

A researcher is cooling a metal. She cools the metal so that the temperature of the metal drops at a constant minutes of cooling, the metal is 390 °C. After 40 minutes, the metal is 110 °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.
The temperature of the metal decreases at a rate of ____ °C per minute.
* As time increases, the temperature of the metal increases.
The temperature of the metal increases at a rate of ____°C per minute.
(b) What was the temperature of the metal when the researcher started cooling it? ___∘C

Answer 1

To answer your questions, we can analyze the data provided:

1. Initial temperature of the metal: 390 °C
2. Temperature after 40 minutes: 110 °C

Now let's calculate the rate of temperature decrease over the 40 minutes.

Step 1: Calculate the temperature change The temperature change is: \[ 390 , \text{°C} - 110 , \text{°C} = 280 , \text{°C} \]

Step 2: Calculate the rate of decrease in temperature To find the rate of temperature decrease per minute, we'll divide the total temperature change by the time period: \[ \text{Rate} = \frac{280 , \text{°C}}{40 , \text{minutes}} = 7 , \text{°C per minute} \]

Now we can complete the statements.

(a) Fill in the blanks:

• As time increases, the temperature of the metal decreases. The temperature of the metal decreases at a rate of 7 °C per minute.
• As time increases, the temperature of the metal increases. The temperature of the metal increases at a rate of N/A (since the temperature is decreasing, this statement does not apply).

(b) What was the temperature of the metal when the researcher started cooling it?

The temperature when the researcher started cooling it was 390 °C.

So the final answers are:

• (a) 7 °C per minute
• (b) 390 °C