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.

Question

(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 analyze the cooling of the metal, we can look at the data given:

• Initial temperature (after 0 minutes): 390 °C
• Temperature after 40 minutes: 110 °C

Part (a)

To find the rate at which the temperature decreases, you can calculate the change in temperature over time:

1. Change in temperature = Initial temperature - Final temperature \[ \text{Change in temperature} = 390 °C - 110 °C = 280 °C \]

2. Time elapsed = 40 minutes

3. Rate of change of temperature = Change in temperature / Time elapsed \[ \text{Rate of change of temperature} = \frac{280 °C}{40 \text{ minutes}} = 7 °C/\text{minute} \]

Now we can fill in the blanks in the statement:

• As time increases, the temperature of the metal decreases. The temperature of the metal decreases at a rate of 7 °C per minute.

Part (b)

To find the initial temperature of the metal when the researcher started cooling it, we can use the information given. The temperature drops from 390 °C to 110 °C over 40 minutes, so the initial temperature (when the cooling started) was 390 °C.

So the answer is:

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