Question

the following situation involves a rate of change that is constant. write a statement that describes how one variable changes with respect to the other, give the rate of change numerically (with units), and use the rate of change rule to answer any questions. a 1 - degree change (increase or decrease) on the celsius temperature scale is equivalent to a $\frac{9}{5}$ - degree change on the fahrenheit temperature scale. how much does the fahrenheit temperature increase if the celsius temperature increases 3 degrees? how much does the fahrenheit temperature decrease if the celsius temperature decreases 25 degrees? which statement describes this situation? a. the celsius temperature varies with respect to the fahrenheit temperature with a rate of change of $9/5^{circ}$f per degree c. b. the celsius temperature varies with respect to the fahrenheit temperature with a rate of change of $9/5^{circ}$c per degree f. c. the fahrenheit temperature varies with respect to the celsius temperature with a rate of change of $9/5^{circ}$f per degree c. d. the fahrenheit temperature varies with respect to the celsius temperature with a rate of change of $9/5^{circ}$c per degree f.

Explanation:

Step1: Analyze the rate - of - change relationship

We know that a 1 - degree change on the Celsius scale is equivalent to a $\frac{9}{5}$ - degree change on the Fahrenheit scale. This means the Fahrenheit temperature changes with respect to the Celsius temperature. The rate of change is $\frac{9}{5}$ degrees Fahrenheit per degree Celsius.

Step2: Determine the correct statement

The statement that correctly describes the situation is that the Fahrenheit temperature varies with respect to the Celsius temperature with a rate of change of $\frac{9}{5}^{\circ}$F per degree C.

Step3: Calculate the change in Fahrenheit for a 3 - degree increase in Celsius

If the rate of change is $\frac{9}{5}$ degrees Fahrenheit per degree Celsius, when the Celsius temperature increases by 3 degrees, the increase in Fahrenheit is $3\times\frac{9}{5}=\frac{27}{5} = 5.4$ degrees Fahrenheit.

Step4: Calculate the change in Fahrenheit for a 25 - degree decrease in Celsius

When the Celsius temperature decreases by 25 degrees, the decrease in Fahrenheit is $25\times\frac{9}{5}=45$ degrees Fahrenheit.

Answer:

C. The Fahrenheit temperature varies with respect to the Celsius temperature with a rate of change of $\frac{9}{5}^{\circ}$F per degree C; The Fahrenheit temperature increases by 5.4 degrees if the Celsius temperature increases 3 degrees; The Fahrenheit temperature decreases by 45 degrees if the Celsius temperature decreases 25 degrees.